1.) It's a very time-consuming and hands-on process to train a surgeon. There aren't many other fields that I'm aware of with the same level of intense apprenticeship as surgery (and medicine in general). My first thought after entering medicine was to marvel at how much effort goes into training a single physician. There is a lot of training at between a 1:1 - 1:3 student-preceptor ratio in an effort to produce very high-quality physicians. So, the solution is not exactly as easy as, "well just make more surgeons."

2.) The federal government controls the number of residency slots each year, through Medicare funding for residency programs. I don't pretend to know the details of how it works, but my impression is that to get more residents per year, you need to convince Congress that it's necessary.

3.) Classic chicken-and-egg problem. Any medical student can go into surgery if they want to, unless their performance up till that point is seriously below par. However, there are many other specialties that offer more attractive lifestyles. So to increase the number of students who choose to do surgery, you'd need to find a way of signaling to students that the life of a surgeon isn't all back-to-back divorces, microwave dinners, and 80-90hr work weeks.