No judge would take a plea bargain without evidence.

Criminologist here. That is absolutely incorrect. The way the system is set up is to charge a defendant with as many charges as possible ('tacking on charges') so that in the 'negotiation' phase the prosecutors can remove some to get the defendant to plea down. We arrest far more people then there is time to try them which is why 90% of cases plea (even when the defendant is innocent). It's between the defense attorney and the prosecutor. Rarely does a judge not accept a plea and no 'evidence' needs to be involved. The purpose of the plea is to convince the defendant that there is ENOUGH evidence to prove to a jury that they are guilty (even when there isn't).