Board Game Arena

Why dose King of Tokyo ask if you want to stay in Tokyo? I don’t see that in the rules (But, I may have over look it.)

That ONLY happens if dice make you lose health. You can set automation options though. Rule does not allow you to lose health on power cards and leave on that.

It is in the rules : you can leave tokyo when you take damages from smashes, so the game ask you in this case

It's the whole object of the game. To stay or not to stay, that is the question.
It is a strategic choice you have to make.