Yes, this is another obvious solution that we could use to help solve this problem. Thank you for the suggestion.
I guess it operates similar to the "Paste from Word" button on Wordpress - because this button both clears the unnecessary tags plus pastes the text itself. Also it has a better name for novice users, I guess: you know that if you click this button, your text will be pasted from Word perfectly fine. But some users may be confused seeing the "Clear formatting" button.
So we will need to make the decision here what exactly we should use to solve this problem. Though again, your suggestion is valuable because it offers an extra option to us :)
