Interesting you'd mention this, since it was just published this month as an idea with a mathematical model of how it would work out:
Article
There are also three editorials about what could be done:
Editorial 1,
Editorial 2, and
Editorial 3
The idea was to allow residents to notify programs if they were "preferred", which each applicant was allowed to do for 10 programs. You could apply to as many programs as you wanted, the rest would not be "preferred". The model assumed that if programs had to review less applications, they would do a more holistic review. What the paper suggests is that allowing this was overall a good -- the only people "hurt" by the model were the top students, they got less interview offers BUT they were already getting so many interview offers that "less" was meaningless, since they couldn't go on all of them anyway.
The editorials mostly support this notion, although also mention the idea of a match for interview offers, limits on the number of interviews, and some other ideas.
My main quibble with the article is how they handled the "preference". The way their model works, each student gets a score from each program and that determines whom they interview and rank. When a student picked a program as a preference, they added some points to their score -- per their description, about as much as 10 points on the USMLE. But what happens if programs decide to ONLY interview applicants who indicate a preference? Then, all we've done is create a system with a limit of 10 applications. (This is mentioned in one of the editorials)