Why aren't clearinghouses used in college admissions?

I recently had an email from  Professor Deepak Hegde, at NYU's Stern School who asked me a question that led to the following exchange (edited for brevity and reproduced with his permission):

"Why are admission decisions in a broader set of settings (e.g., Phd applicants-programs, MBA applicants-to-business schools and so on)  not cleared through matching programs as is done with medical schools and residency applicants (or in some cases public schools matching)?   Are there a general set of conditions that one could develop to understand the contexts in which the matching algorithm that have helped advance could be implemented effectively?"

I replied as follows:

"I certainly don’t have a complete answer, but one obvious piece is that setting up a centralized clearinghouse for a whole market involves getting a lot of parties to coordinate and cooperate.  So I would guess that MBA admissions have a better chance of getting organized than, say Ph.D. admissions, since MBA programs are more alike one another than are Ph.D. programs (e.g. in Physics and Philosophy, or Chemistry and Chinese).

"And since wide scale cooperation is hard, I think it mostly happens in market in which people are very dis-satisfied with the existing system, and not just somewhat irritated.

"Is it your sense that MBA admissions is in a crisis of some sort?"

His reply: "In my assessment ... MBA admissions is not facing such a crisis, yet."

So...I think the MBA Match isn't something we'll hear about in the near future.