I'm also going to agree to what everyone else said. If they did not think you would make a good addition to the program, they would have rejected you rather than waitlisted you. Right now you just have to be patient. Have you asked how the waitlist works? Is it ranked or not? If it is, can they tell you your ranking? Moreover, regardless of how the waitlist works, it will not be used until after admitted students turn decline their offers, which means at this point in the application season nothing you do can really increase your odds of getting in. The only additional email you should send out at this point are ones to let the program know about other offers, ones to let the program know if you win any awards, and possibly one in April reiterating your interest in the program and letting them know it is your top choice. Other than that, it is a matter of chance.
Last year I was wait-listed at my top school and also told that my program historically used its waitlist. When I found out that I was waitlisted, I emailed my POI to let him know I was still interested. I emailed him again in mid-March to let him know I was still interested in the program after he asked if I wanted to remain on the waitlist and if I had any other offers. Finally I emailed him once again at the beginning of April to let him know that I still had not accepted any offers, that this program was my top choice, and if offered admission I would accept. I was offered admission shortly after that last email. I know being waitlisted at your top school is incredibly difficult and anxiety inducing. I felt stuck in some perpetual limbo. I was constantly afraid that I would open my email and find that I had been rejected. I just wanted to get in so badly and was there was nothing I could do to ensure that I would be admitted. I know you are really eager to get in to this program, but unfortunately for the most part your admission from the waitlist is a game of chance and there is little you can do but try to be patient.
While I'm not one to enjoy the misery of others, sometimes people do such a good job of combining heartbreak, disdain, and criticism, they create an epic rejection result post. Here's my personal favorite, someone rejected from Stanford GSE:
That pretty much sums up how I'd feel too. When I'm obsessively checking the results page, I often see this post and it makes me chuckle. It passes the time, and at least their loss will not have been in vain.
