Admissions has to target a fixed number of students each year, plus or minus. Students have to decide where to attend in a narrow window. If you accept a lot of students who are unlikely to attend then you would undershoot your admissions target and have to try to convince students to attend in later rounds of admission, but that’s too late because they’ve already decided to go somewhere else.
It’s not really a risk to overaccept if you know what % will commit.
Idea: When you apply for a college, you have to prepay for the first semester. If you get admitted, you have already paid for the first semester. If you get rejected, you get this advance payment back. On the other hand, if you get admitted, but decide to go somewhere else, you loose money.
This should give the university a strong incentive not to reject strong candidates that will go somewhere else - quite the opposite: if you admit such a candidate, but the candidate goes somewhere else, the university earns even more (the semester fee without having to provide any service for this money).
Perhaps insurance companies could create an insurance product to insurance the applicant against the case that he gets admitted at many colleges and thus has to pay many, many times the semester fee (or application fee).
Insurance premiums would be a significant fraction of the average tuition, which would be beyond the reach of many.
The effect of the proposed system would be that most people would just apply to one school. If rejected they would try another next year, if they haven’t given up on college, and so on.
Of course, there's no way to get schools to all require a deposit, and even if there were schools would give fee-waivers to low-income students (giving them an advantage over middle-class kids).