Okay, @manyloyalties makes some strong points (BTW, did you go to medical school? Not being argumentative. If not, it sounds like you still know a lot, much more than an English major like me ).
But shouldn’t we bring up the unmentioned (or it probably is mentioned, but there are so many posts in this thread!)? We all know that the ground is littered with the bones of once-hopeful pre-med students. We all personally know friends, family members, and classmates who started out pre-med but switched to another “major” (pre-med, of course, is not a major). One friend of mine who attended UIUC became pre-law. My roommate in college went to dental school.
Clearly, the OP is bright; otherwise, he wouldn’t have been admitted to Yale. Any idea how many Yalies get weeded out? I’m not questioning the OP’s devotion or desire, but if medical school at some point is not an option, what should he do? Is Yale still worth the 60K (plus his family’s substantial payment) because it can open doors? If the OP’s plan is to immediately enter the job market, maybe? The starting salaries from top schools are higher (don’t worry, people, the other grads from other schools catch up over time). Also, there’s the trend (disturbing, IMO) of how Wall Street poaches all sorts of Ivy grads (not just economics grads) for two years of grueling but well-paid work. These students get run through the mill, working 80+ hours per week, and essentially lose two years of their lives and often regret the decision after. But they do get paid a bundle.
If med school does not pan out, Madison is perhaps the stronger choice if the OP plans to go to grad school, which is far less dependent on the name of the undergrad institution. He can get into a top STEM grad school program via Madison or New Haven.
Thoughts?