There is little doubt that having mandatory minimums actually slows down the court process. There are enormous backlogs now because of COVID-19, so removing as many mandatary minimums as you can should ease some of the pressure on the court system.
The reason why it delays the court processes so much is that people don't want to plead out. They don't want to plead to something less, because the mandatory minimum is fixed there, and so they have a tendency to want to contest and plead not guilty, rather than go by route of some sort of arranged settlement for something less than what they are charged with, which is often the way it goes when there isn't a mandatory minimum.