The thing is I've already been accepted to two NYC med schools, both of them "encourage" MD/PhD applications while in your 1st and 2nd years of med school (NYU an MSSM) and I am currently waiting to hear from Cornell (March).
So we will see...
While Cornell doesn't solicit general applications to the md/phd program, if a strong interest is demonstrated (as I mentioned above), then the director will give you specific advice about how to go about the process. You may want to ask him about the prospects given your application before you choose to attend or not, he is very forthright if he is in the position to give you an answer. In some cases, if one did not have a competitive application during the regular cycle, being an in house candidate may not help that much, unless the issue was too little research experience, or other aspects that can be strengthened during medical school.
Since our medical school class is 100 people, and MD/PhD's make up anywhere from 12-17 people a year, there isn't a large impetus to increase that number for the sake of having a larger MD/PhD population; money for spots isn't a rate-limiting factor. There is a large investment both monetarily as well as in advising, support, trouble-shooting if problems arise, pointing out opportunities that are specific to student interests, and the program wants to make sure that there is a reciprocal interest in the aim of the program.
There are, of course, many cornell medical students who are not in the program, both by choice or otherwise, who have a strong interest in academic medicine (clinical interests are a given, but there are quite a number with more basic/translational career interests) and have been very happy with the research opportunities. The Tri-Institutional community is still open to all students, and students have spent time at all of the institutions (and their off-shoots, including the Aaron Diamond Aids Research Center) during med school, in the summers, or by taking a year away (through HHMI or otherwise).
As for attending Cornell med over NYU/Mt.Sinai/Columbia - I'd simply go with the school you like the most, whichever it is. It isn't trivial to join MD/PhD programs anywhere, given the large investment made in the student. But at each of those schools, there are students who do join regularly from the MD pool.