People don't like how it gets scuffed up and cloudy. Personally, I generally leave it in place and clean and buff, unless there are issues with edges peeling up or bubbles. I really don't want to deal with the removal process and the potential paint loss if there's nothing really wrong with it. The enemy of good is better, as the saying goes.
As for why people don't want to put down *new* mylar, I have no idea. I always put down new mylar in high wear areas, and it's nearly invisible. I guess some people say that the game plays differently with mylar on the playfield? I can't say that I've ever noticed a difference. But, I'm just a casual player and not really a tournament player.