One (modest) force that coerces the market: you nearly always must attend law school. Unlike Lincoln, John Adams, Marshall, et al, you have to get a degree from a law school in order to become an attorney. Apprenticeship is peanuts compared to getting a degree (provided you can find a sponsor). There's a handful of US states that still permit apprenticeship, but most do not.

Ok, then why is law school so expensive? It seems to me that classes could be offered online without practical problems, and exams could be organized on a national level.

The market isn't failing; that's the market rate!

The market is not failing to determine a market rate. The market is certainly failing to provide equal access to the legal system.

Or rather, the legal system is preventing the market from accessing it, e.g. there are something like 2 U.S. states in which one can currently sit for the state bar without having been awarded a JD.

This is the market working; the market itself is thus a problem too.