I don’t think we can really make this claim. Life which forms around less stable stars may adapt if there is enough time for them to do so. It’s also important to note the sun is not the mean star. The vast majority of stars are red dwarves which, while more variable, are much longer lived.
“On Earth” is the problem with the argument. If any alien life exists, the one place it isn’t is Earth. A super-Earth in a Goldilocks orbit around a K1V star would keep atmosphere and water for longer.
Eventually they too will become uninhabitable, but the relevant question about alien life is not “eventually” but rather “now”.
