The loser of every suit will simply always appeal the AI decision, thus requiring a human decision anyway.

AI would review the appeal so that only things which require human decision receive human attention.

And we trust the AI to reliably decide what requires human attention because...?

Because modern LLMs are capable. Even if they make a mistake by appealing you can clear it up and convince it why there actually is an argument than it being able to be resolved by just reading the contract for example.

There's still inequality in someone else receiving a false positive approval from the AI while another gets rejected. Equal treatment and stochastic systems don't mix.

The law is already a stochastic system and it's designed to eventually receive a result that is correct most of the time. It doesn't try to be 100% correct. Not having it be 100% correct does not cause society to fall over.

Exactly. Not to mention that there is no reason a well-calibrated AI system cannot be Pareto-optimal over the human-only system.

For example if you are interested in bias, an AI system can be backtested; new policies applied on old data, and whatever metric for inequality you are investigating can be measured.

You can’t backtest a human.