So no one is going to do anything about this but us. The ABA certainly isn't interested in anything that may cut highly-paid law dean and university professor positions. Law professors themselves have AALS, which is constantly lobbying for more student loan pork to be trickled up from poor students to wealthy law deans and professors. Law students have no bargaining power regarding the current situation, so nothing is ever done in their interests.
Obviously, you can't unionize students, as they are not employees, but you can build an organization that uses collective action to advocate in their interests. If students collectively decided to protest one year--say they would collectively refuse to sign their Fall FAFSA forms, unless tuition was reduced by X%, you would definitely see a bunch of universities start to listen. I'm sure there's a million people on here who will berate me and tell me that this is stupid and that it will never work--and I just have one thing to say to them: You are right, I am stupid, and this will probably never work. I am just bored and running out the clock on my day of "volunteering."
However, there are a few reasons why this will work. Namely:
1) When workers engage in collective action, there's a lot of potential replacements out there. It's easier to replace a worker, because there's almost always more workers than there are jobs. But if a student refuses to pay tuition, especially if they are upperclassmen, there's no pool of replacement students readily available for a school to admit instead.
2) A student pays the school, whereas the employer pays the employee. Thus, in the event of a "strike," it's the school losing money--not the students. The financial pressure is on the school to cave, not the students.
3) You don't even have to win majority support for collective action to have force. You don't have to win an election. If only 25% of students partook in this behavior, it would be devastating to a school's bottom line. And judging from how angry the students were at my school about tuition hikes, getting support from 25% of students would seem to be low-balling it. And I went to a "T20" school, so I'm pretty sure things are not better below that threshold. Most people still there after 1L seemed jaded and trapped by their sunk costs and/or the expectations of their families/friends, and probably would think of it as a favor to them if the law school kicked them out.
4) Law students are highly engaged online on Facebook, blogs, etc., which makes it much easier to recruit people to the cause. Also, joining in on the protest takes very little effort at all. Actually, it takes negative effort, since all you would have to do is collectively refuse to sign FAFSA forms for the upcoming year.
5) Everybody wants tuition to go down, including practicing lawyers (that can't afford to pay people enough to pay down debt) and a lot of law professors that actually have a twinge of self-awareness and a conscience. The problem is simply one of collective action: if one school alone lowers tuition, they put themselves at a competitive disadvantage. But if students were organized, the schools that DON'T lower tuition would be the ones at a disadvantage.
I'm sure there's a number of other reasons to deride this idea, but I feel like at least thinking about starting some organization to advocate for this is a better use of my time than what I'm currently doing right now--(i.e. the bar has been set pretty low). Law School Transparency has done a good job in and of itself on correcting the information imbalance out there about job prospects. But tuition is still to high at law schools, and it needs to go down fast. It's not good for anyone. And obviously, this idea can be expanded not just to law schools, but nearly every over-priced degree program out there, including undergrad degrees.
But the bottom line is that this:

is unsustainable, unjust, and untenable in both the short-term and the long-term, and clearly nobody in charge is interested in doing anything about it. So we must.