Meh, not really. It seems really low, but it's not. The average applicant sends like 60 applications, it's patently absurd. The only thing that would change under an application limit of 12 is your application to interview yield would be much higher. There would be problems at first, and maybe something slightly higher is needed, but 1 extra application would go a
long way, longer than you would think. It doesn't work that way now because the vast majority of applications sent from a purely system point of view, are pointless. Any application that gets sent and doesn't lead to you ranking a program, and that program ranking you is pointless. That's why overapplication is such a problem, it's literally a waste of everyone's time, and because it costs 50$ to send JSON strings apparently(AAMC non-profit lul): money. Look at the PD
pain points survey by the AAMC, almost half are the direct result of overapplication.
Large Volume of Applications? Overapplication.
Lack of information about which applicants were genuinely interested in my program? Overapplication.
Applicants cancelling interviews? Overapplication.
Interview season too long? Overapplication.
People feel the need to send so many applications is because everyone else is sending so many applications. But if everyone sent less applications, everyone else wouldn't need to send so many applications and the match rate would be the same.
Bryan Carmody has a pretty good breakdown of this. It seems counter-intuitive, but it works.
An application limit makes the match and the people behave much more predictably. Students are always going to send the maximum number of applications, and spend most of their applications applying programs they perceive as having the highest possible chances of getting an interview at and therefore ranking. Program directors have a much easier time deciding who to interview because they will receive far fewer applications than they used to. It makes it easier for programs at lower-tier programs, because they don't have to do anywhere near as much guesswork about who wants to come to their program. If PD's aren't getting enough applications, they can take pizza to the nearest medical school: it's not brain surgery.