I don’t see how that helps?

A lawyer isn’t going to sign on to take liability risk unless they spend quite a lot of time analyzing the AI’s outputs for possible blunders?

So it structurally can’t cost significantly less.

Lawyers normally don't have any liability risks, no? And reputational risks are very limited, a lawyer can always point to a judge, to the other lawyer, to circumstances, and away from their own (or the AI's output) blunder.