This is something important to note. The AVMA does not have the ability to force schools to cap student numbers, as much as we would like them to be able to.
The other problem is that, as far as I know, the AVMA can't just refuse to accredit a school if said new school meets accreditation criteria just because they (the AVMA) don't want any more schools. It would be akin to (not a perfect comparison, but bear with me) NAVLE refusing to license/pass more students than some cutoff number of total test-takers just because they want to keep numbers down, even though the "excess" students also passed the exam. Their job is to maintain quality of education like dyachei said, not "quantity" of education if that makes sense.
It's kind of a ****ty situation overall. Right now, the AVMA seems to only have the authority of an advisory body...which was its original intent, but given the economic issues happening in the profession....