we know from direct, first-hand experience that the current adjunct faculty situation actually does work to a certain extent--
This is what I mean? Work how? For whom? To what goal? Is it advancing the long term goals of the school? If the only goal was to reduce the budget I have a lot of suggestions for you. Fire all the people making high salaries and replace them with people without doctorates, increase class sizes and don't pay more per class. I suspect you would say that this would reduce the value of the education and send the college into a death spiral, but if that is true why is hiring people to teach large numbers of classes in conditions in which they can't do all the things full time faculty members do not creating this same thing in slow motion?
It works for each individual institution in whatever way that institution expects it to work. The goal of hiring adjunct faculty is to serve the needs of the institution.
It is not to provide jobs for adjunct faculty.
The institutions that hire part-time faculty to "teach large numbers of classes" need those people to teach those classes; generally speaking, they don't need them to do anything else. The places that use huge numbers of adjuncts have decided, for whatever reason, that they don't need FT faculty teaching those particular classes, or that they have enough FT faculty to fulfill whatever other needs FT faculty serve at the institution. So no, presumably, it's not doing "the same thing in slow motion."
I've been in charge of a very large freshman comp program; we analyzed our use of adjunct faculty from a lot of different angles, and what we decided was to get rid of them and replace them with closely-supervised graduate teaching fellows. In that instance, we determined that our institutional resources were better spent on having people teach those classes who had a different kind of relationship with the institution. Had we not had a suitable graduate program, we probably would have created a few FT/NTT positions to teach nothing but comp and world lit instead. The institution, in other words, decided that that particular use of adjunct faculty was not helpful to its long-term strategies so we did something different.
market forces may not do what you want them to do, but that doesn't mean they're not at work in every situation.
Market forces are invoked as if they were some sort of natural law, which they aren't. They are just an annoying trope that can be taken out and shook around whenever anyone asks whether there might be a better way to do do anything. But never mind that angle. Just a cursory look at how adjunct salaries are determined would tell you that this is a ridiculous idea. Some schools pay as much as 6 times as much per class as other schools? Are those jobs harder to get? Not really? Do they go to more qualified people? Not necessarily. It isn't an open market at all...
If we can hire excellent faculty who achieve the goals we seek to achieve for $XXXX per course, market forces are, in effect, a natural law. No matter what you think, colleges and universities are usually not run by stupid people (and in fact, they are usually run by people who came from the faculty); if the cost/benefit analysis showed that the school was losing more than it was gaining through its use of adjunct faculty, that situation would change. The economic effect on part-time faculty is a part of the calculation, but, sorry, from an institutional perspective it's far from the largest factor.
And as for your differences in salary, try comparing across single locations, and see how the differences in salary map on the qualification of the adjuncts and you'll see that you're wrong. It's useless to compare salaries across regions because the local situations are so hugely different--so comparing what a SLAC in the rural Midwest pays with what NYU pays doesn't make any sense.
In my previous rural state, all the small private colleges paid pretty much exactly the same for adjunct faculty, which clearly suggests a market at work; the research universities in the state paid significantly more, particularly in disciplines like business, for which they indeed did get faculty with better qualifications--again, the market at work. And hiring for those part-time positions was massively more competitive than it was at the SLACs as well.