Let's look at this systemically...where can change be implemented (top to bottom):
Licensure: State licensure laws are too cumbersome to change across the board (each state would have to enact legislation). I'd love states to make this push, but it will cost too much money, and we all know that psychologists are already very stingy with political contributions (just look at the public data on campaign contributions, PAC funding, etc).
Postdoc: Some states have waived them, so changes would only apply to most but not all states. If someone wanted to be crafty they could limit who is allowed to acrue post-doc hours in a particular state (students from APPIC/APA acred sites). This would only really be useful in CA, NY, and a few other places, and it would be viewed as punishing the student.
Internship: Right now we have 2 system at play: APPIC and Non-APPIC. Each year more and more people are bypassing APPIC for Non-APPIC choices. This is the first logical place to make changes.
Program: If a program requires their students to complete an APA-acred or APPIC-acred internship site, that would functionally remove non-APPIC options...with no policy/law changes. In fact, this is already the case for the majority of doctoral programs. The programs who do not have this as a requirement will most likely not make the change "for the greater good". However, if the APA makes this a requirement for APA-acred...that could change things. This change will open up malignent programs to possible lawsuits from their students who are unable to match to an APPIC/APA-acred site, though that isn't necessarily a bad thing for the profession as a whole. I am sure there are other changes to the APA-acred. standards that would fall under "professional requirements", though it would take a strong APA to enforce the changes....which is its own problem.
Some people have cited anti-trust laws as a possible barriers to major restrictions in programs. I'm not a lawyer, so I cannot comment on their applicability, but I'm sure there is enough grey area that people would threaten legal action. I'm also sure there is enough "professional latitude" to allow for increases in APA-acred standards that would fix most of these problems. You may not be able to set caps, but there are other ways to limit programs.
Admittedly, any restriction to a program or the internship process will "squeeze" current students. A transitionary period is needed to allow students currently in the system to get out before such sweeping changes are enforced. I think changes need to be made ASAP because more and more people are going to be funneled to non-APPIC sites, and that threatens quality control, floods the market, and weakens our standards as a profession.