Euler17

People leave their PhD programs with an MS all the time.  I would be utterly shocked if your program did not allow this.  Talk to your advisor/the grad program chair and figure out how you can stay and leave with an MS.  Your first year of courses is probably the same, so even in the worst case that they cut off your assistantship, you'd still save money compared to starting over somewhere else.
You can re-apply and I'm sure you'll have a lot of success, but really ask if that's the best path for you.  I'd do anything I can to try to make it work at your current program to leave with an MS, which will save you lots of time and money.  And you go to a top program, so it doesn't make sense to transfer down.

OP should ask Michigan directly about the quals, rumor has it they may be changing. 
I think the idea that Michigan stat genetics is facing a steep decline is a bit misguided. They have some strong junior faculty working in diverse areas.  Also, they have some nice recent hires, like Veera Baladandayuthapani, who doesn't strictly focus on genomics, but has done some really innovative work. 

I'm not sure that I agree with this. Hyde Park / Kenwood are really nice areas in Chicago, right of the lake, good nightlife, etc. The areas surrounding these two neighborhoods may not be nice, but the immediate Hyde Park area I think is really nice.
Disclaimer: from the area and lived in the city for 4 years, so maybe biased.

In relation to you not being proud of your recent papers, remember that you probably know the shortcomings/holes in your work better than anyone else. I have struggled with being completely unsatisfied with 2 of the papers I wrote this year because I felt like there were so many ways that they could be improved, but I trusted my professors that they were ideas worth writing about. And maybe I don't get around to improving upon them in later papers the way I envision, but once they are out there others have the opportunity to build on them if they'd like. I def agree with most of the issues you bring up, just wanted to give my two cents on that point. 

In relation to you not being proud of your recent papers, remember that you probably know the shortcomings/holes in your work better than anyone else. I have struggled with being completely unsatisfied with 2 of the papers I wrote this year because I felt like there were so many ways that they could be improved, but I trusted my professors that they were ideas worth writing about. And maybe I don't get around to improving upon them in later papers the way I envision, but once they are out there others have the opportunity to build on them if they'd like. I def agree with most of the issues you bring up, just wanted to give my two cents on that point. 

I have definitely felt this strongly and had previously had some years of a similar identity crisis before ultimately deciding to return to the statistics/data science world.  Like you, I entered graduate school for the first time with a very idealistic attitude.  I found the "creative/beautiful ideas of bridging theories" incredibly exciting -- when I'd learn some new piece of theory, it would fill a piece of this large puzzle in my mind thatI was trying to assemble of what would someday become the full knowledge of the field of statistics.  I was succeeding in my research, but also felt like it was not very serious and that someday I would get to the "real stuff."  I thought that the "real stuff" was just hidden behind a few more layers of math and foundational material that I didn't know yet, but all these problems were possible to overcome if I just learned a few more things.  The people in Annals of Statistics were certainly doing the "real stuff," I thought.  But I think eventually you sort of see through these things and realize that there is no "real stuff" and that statistics, for the most part, is a field with a lot of paradigms and ideas but so much complexity that you are in many ways destined to be unhappy if you have both 1) your idealism for the truth and 2) your moral qualms about the quality/arbitrariness of so much research.  This is especially true in industry where you are often asked to answer impossible questions or being encouraged to produce results that your bosses prefer rather than the truth.  I certainly know others who have felt this way as well.
As for how to deal with these feelings, I think your advisor has a lot of good advice.  Don't view your PhD and your potential professor jobs afterwards as solely a quest to answer the deepest questions of the universe -- maybe you can do some of that, but you're in training to gain a set of skills and gain the qualifications that lead to more opportunities.  Maybe you're not doing what you want, but honestly, you're probably not having a meaningfully *negative* impact on the world if you view your work as slightly shoddy.  In fact, that you're even thinking about these problems means that you are useful in improving the culture of the profession, especially in industry where it is more difficult to succeed with this kind of skepticism.
In reality, what are your career options if you leave the field and how much are you willing to sacrifice?  Will you discover a different set of problems there?  I suspect so.  I decided that even if I'm not going to come up with the perfect theories, I can still learn some interesting things and work on cool problems.  I can try to stay true to my morals and not do things that are actively harmful.  Being in academia lets me teach.  This forum allows me to try and help people in the field.  And I get to make a living (and a very good one at that) doing something that I have already invested a lot of time in and have a lot of knowledge in, and I don't think it's worth throwing that away because it's not exactly what I expected.  

This doesn't address everything in your post, but something to maybe keep in mind: I've found men to be much less forthcoming about their struggles in school, especially in a competitive grad school environment. Additionally, men, like myself, have been systematically "affirmed" by society of their ability to perform in STEM programs, which gives many a confidence that is often misplaced. This is just to say that when you are taking the "temperature" of your classmates, the observed states of men are probably less informative of the hidden states than they are for other students(excuse the hidden markov model terminology). 
 
 
Edit: As an aside, covid-19 is definitely exacerbating inequity in academia. I have also found, like most others, I struggle much more in online math and statistics classes than in in-person ones. I hope you can stick it out until things return to a more "normal" situation. 

How sure are you of those research interests and how passionate about them are you?  Some people can be truly fulfilled by their research and if that'll make you happy, go to Berkeley.  But you're not even going to be able to do good research if you're unhappy and wishing you were on the other side of the country.  Are you sure that you are that much interested in probability than say, MCMC, where you could work with Xiao Li Meng at Harvard who to me is one of the most interesting people in statistics - just read some of his paper titles and listen to his talks.  Are you sure that theoretical machine learning at Berkeley is that much more interesting to you than the reinforcement learning that Susan Murphy is doing?  There's plenty of theoretical stuff going on at Harvard that might satisfy you intellectually, and I definitely think that location is extremely important.  The facts are that you will be qualified for top stats jobs after working with someone good at Harvard.  Maybe Berkeley will offer you a slightly better chance at doing the type of ML that gets a FB research job, but is that extra slight chance worth 5 years?
My recommendation would be to download some papers from profs you like at both school.  Read the papers from Berkeley and ask yourself if you love reading about that subject so much that you would move across the country to Berkeley to be able to ask the person who wrote it a couple questions every week.

This doesn't address everything in your post, but something to maybe keep in mind: I've found men to be much less forthcoming about their struggles in school, especially in a competitive grad school environment. Additionally, men, like myself, have been systematically "affirmed" by society of their ability to perform in STEM programs, which gives many a confidence that is often misplaced. This is just to say that when you are taking the "temperature" of your classmates, the observed states of men are probably less informative of the hidden states than they are for other students(excuse the hidden markov model terminology). 
 
 
Edit: As an aside, covid-19 is definitely exacerbating inequity in academia. I have also found, like most others, I struggle much more in online math and statistics classes than in in-person ones. I hope you can stick it out until things return to a more "normal" situation. 

This doesn't address everything in your post, but something to maybe keep in mind: I've found men to be much less forthcoming about their struggles in school, especially in a competitive grad school environment. Additionally, men, like myself, have been systematically "affirmed" by society of their ability to perform in STEM programs, which gives many a confidence that is often misplaced. This is just to say that when you are taking the "temperature" of your classmates, the observed states of men are probably less informative of the hidden states than they are for other students(excuse the hidden markov model terminology). 
 
 
Edit: As an aside, covid-19 is definitely exacerbating inequity in academia. I have also found, like most others, I struggle much more in online math and statistics classes than in in-person ones. I hope you can stick it out until things return to a more "normal" situation. 

This doesn't address everything in your post, but something to maybe keep in mind: I've found men to be much less forthcoming about their struggles in school, especially in a competitive grad school environment. Additionally, men, like myself, have been systematically "affirmed" by society of their ability to perform in STEM programs, which gives many a confidence that is often misplaced. This is just to say that when you are taking the "temperature" of your classmates, the observed states of men are probably less informative of the hidden states than they are for other students(excuse the hidden markov model terminology). 
 
 
Edit: As an aside, covid-19 is definitely exacerbating inequity in academia. I have also found, like most others, I struggle much more in online math and statistics classes than in in-person ones. I hope you can stick it out until things return to a more "normal" situation. 

I see biostat admissions getting more competitive, not because incoming classes are getting smaller (though in some places they may be, somewhat) but because of increased interest in the field of biostatistics due to COVID. Nationally, applications to schools of public health are up about 20%, and while a good chunk of that is in other fields (hello, epidemiology!) there's definitely a spillover effect into biostat. Anecdotally, we're seeing a higher proportion of applications from people whose profile can be summed up as "I'm a smart person who didn't intend to go into biostat but gee that sounds pretty cool so let's give it a shot".

If you are applying to TAMU because it is in Texas, I would also look at UT MD Anderson's biostatistics program. They have a solid reputation and most of the talks I have heard from faculty from their have been interesting. 

If you are applying to TAMU because it is in Texas, I would also look at UT MD Anderson's biostatistics program. They have a solid reputation and most of the talks I have heard from faculty from their have been interesting. 

We used Agresti foundation of linear and generalized linear model. I feel that it is a bit cumbersome and wordy but in general a good book in terms of mathematical rigour. A lot of details regarding different models are not useful for me but I did learn some very useful techniques and practiced calculation quite a bit.

Plane answers is a good book, I've used that one. Primer to Linear Models (Monahan) is good, as is Linear Models in Statistics (Rencher). I also really like the discussion in KNNL, personally.

The classic book for linear models in a PhD program is Christensen's Plane Answers to Complex Questions.