Good questions.
1) Why does a PhD program in the U.S. last so freaking long?
I think previous replies hit the nail on the head here. For many programs in the US, it's assumed that most students don't have a Master's degree going in, and there's a pretty rigid track you need to follow to graduation. For math, the first two years typically involve hitting the classes hard - and then passing two or three rounds of difficult qualification exams. You'll also begin TA-ing in this time. Beginning in the second or third year, you properly begin your research and spend the rest of your time becoming an expert in your field.
2) Why do so many of you apply to so many programs?
Because of the high number of applicants to each program, and the subjective nature of acceptances into each program. For example, I'm applying to Applied Math programs with a mixed background in math and engineering. Some schools look favorably on the engineering experience, while others consider it a waste of time. And, if you manage to get accepted into multiple programs, you have the luxury of factoring lower-priority factors into your decision, like location and stipends. I am very happy that I applied to as many programs as I did.
3) Do all of you really want to go to grad school? Like really? Or is it because it is the next logical step?
Yes, I really do, and I completely understand your perspective that most students flow right into grad school because working scares them. I was concerned about these biases in myself, and thus after graduating, I spent two years in industry to ensure that I wasn't just doing what seems easy. This was a great move for me, as it allowed me to develop all kinds of skills that one doesn't learn in school (especially very practical programming skills), and also allowed me to pay off my student loans. At the same time I became increasingly convinced that furthering my education is the only way for me to work on the awesome academic problems that interest me... to the extent that I would probably run away and become an Alaskan Bush Person if I weren't accepted anywhere.