Because you are wrongly assuming the new manager will be better.
When Mourinho came in for Poch, he got Poch's side knocked out of the Champions League. Poch deserved a right to stay until he was knocked out of the Champions League himself. When Mason came in for Mourinho, he lost Mourinho's side the League Cup. Mourinho deserved the chance to lose that himself too because you never know he may have won or lost. When the backroom staff came in for Conte, they lost Conte's Champions League place. Conte had a right until the end of the season to do better himself again.
These are three easy examples that don't fit what Ramos, Redknapp, or Conte did when they took over in terms of definitely improving in one competition at least. Perhaps you can argue that the earlier the change is the better, but my argument is always that it has a 50% chance of working and it costs more and you never know. The chairman backs the manager for a full season at the start of the season but never sacks himself or his players mid-season, which is hypocritical. If he held on to his managers through poor league form he would get an honest assessment of himself instead of selling the best players and going for a new manager quick fix every time.
It's like saying why not cheat on your wife. Well, why not stick to your word as a businessman.