> I don't think it demonstrates deference to authority to say that it makes sense that your average judge is likely to be more invested in your average trial than your average jury

First off averages aren’t good enough here.

Second I can’t imagine a better example of an appeal to authority.

Trials are an administrative action. Interest in the process is no indication that the outcome will be just.

Your idea falls apart for all of the reasons an appeal to authority is a fallacy.

Additionally you’re fundamentally changing the nature of society by holding the people accountable to power rather than each other.