Sure, but I'm not sure how AI would solve any of that.

Any claims of objectivity would be challenged based on how it was trained. Public opinion would confirm its priors as it already does (see accusations of corruption or activism with any judicial decision the mob disagrees with, regardless of any veracity). If there's a human appeals process above it, you've just added an extra layer that doesn't remove the human corruption factor at all.

As for corruption, in my opinion we're reading some right now. Human-in-the-loop AI doesn't have the exponential, world-altering gains that companies like OpenAI need to justify their existence. You only get that if you replace humans completely, which is why they're all shilling science fiction nonsense narratives about nobody having to work. The abstract of this paper leans heavily into that narrative