I think the principle is, the game is played by the players and not the umpires. That’s probably why we never see umpires make a call and then just stop play to change their own call. They require the players to appeal the call instead, if they think the play was called wrong.
I remember a softball game in which I crossed the plate to score, and then after a couple seconds the umpire yelled that I was actually out because I hadn’t touched the plate. Setting aside that I don’t think he saw it right, it’s not as though anybody on the other team chased me to tag me out, or told him I missed the plate, or anything like that. He just decided to call me out, period. I’m shocked none of us pushed back on him in the moment, but the rule in the book is, if a runner misses the plate, he’s considered safe until someone appeals, then the umpire rules as he thinks he saw it happen in the moment. It is explicitly an appeal play, and I believe that’s because of the principle that the play on the field belongs to the players, and not the umpire.
The umpire is not there to rule the players like a king. He’s there to adjudicate the rules like a judge.