While lawyers should definitely be reformed, I’m not sure if this would be any different than what we have now. Governments can selectively assign high skilled or interest conflicted lawyers to certain cases (or the opposite for a losing outcome on purpose).

The parish system in Catholicism might be an interesting place to look at. Unless you have a specific skill (such as language, cultural), you’re basically reassigned to random churches every few years. And even if you do have those specific skills, you’ll be reassigned to random churches within those communities. This lottery system would also mean, in theory, that providing high quality and accessible legal education to aspiring lawyers would be in the interest of everyone because some millionaire’s lawyer will have a similar education to yours.