I've seen no evidence that "humanity" is going to be improved. I've seen lots of evidence of the gradual enshittification of everything and a few people getting really rich.
I can think of one: If they can improve AI such that it doesn't cite fictional case study, poor people might get actual/better representation in court. The majority of court cases aren't particularly novel or unique (driving without a license, speeding, public intoxication etc). If we can train AI to do a better job than overworked public defenders, we might actually take a step in the right direction towards giving poor people a fighting chance in court.
I think the more likely scenario is you entrench a two tiered system of justice where now "poor people" are just at the mercy of an AI that replicates existing outcomes.
Instead of trying to slap a technical fix onto that problem, we could be working to address root causes.