Also, no study I am aware of has ever shown that a new coach bump is a real thing. Sometimes new coaches do better. Sometimes they do worse, and sometimes the same. Any belief that they usually improve things is mostly yes, my favorite, confirmation bias. Also there is at least one study that showed that a cohort of instances where the team did improve represented nothing more than a reversion to the mean.
As to your point about the players not wanting a change, DC United fired a coach because the players revolted and demanded it even though he had them playing well for their talent level. The new guy is 2-5-2 for 0.89 PPG. The guy they fired had a +1 GD over 40 games. The new guy has managed to accumulate a -8 GD through 9 games. Their xG also is way down. So their results suck, and their actual and expected numbers are both worse. But I suppose the players are happy now. They got what they wanted. Good for them.