Well, the system would have pro's and cons. Probably the biggest con would be that wait lists would be almost useless. Since everyone is "stuck" with whatever school they matched into, there's no real hope for ever getting into other schools and for those that don't get in (which would leave A LOT of applicants "unmatched"), they can't really bank on a wait list that moves.
There also won't really be a "SOAP" version because unlike residencies, every medical school would let you be a doctor so it's in every student's best interest to rank every school they interview, including the one(s) they hated. Also, most residents have multiple interviews and can "rank" multiple programs while there are a lot of applicants that may only get one or two interviews and the "match" won't really benefit them as they're banking on one school to rank them high enough to get in.
I guess my main concern is just that wait lists would be useless and you can end up with a lot of people who dislike their school choice. Waitlists give people hope and there are always stories of people being accepted 1 week before orientation.
I prefer the current system, but I can see how some people may prefer a matching system.