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.