It not the paychecks that influence federal judges; these days it's more of quid-pro-quo for getting the position in the first place. Theoretically they are under no obligation but the bias is built in.

The problem with a AI is similar; what in-built biases does it have? Even if it was simply trained on the entire legal history that would bias it towards historical norms.

I think it is usually the opposite - presidents nominate judges they think will agree with them. There’s really nothing a president can do once the judge is sworn in, and we have seen some federal judges take pretty drastic swings in their judicial philosophy over the course of their careers. There’s no reason for the judge to hold up their end of the quid-pro-quo. To the extent they do so, it’s because they were inclined to do so in the first place.