For one thing, I think that's overthinking it and just an assumption, I don't remember that ever being mentioned as a genuine threat. It reminds me of when people try to power scale in DBZ using planetary density as factors, as if Toriyama actually considered Planet Vegeta's density so nerds could apply real world physics to Frieza's feats. I'm inclined to believe that even if that's a logical assumption as to what would happen in real life with a Rumbling that it wasn't a serious consideration by Isayama at the time.
For another, that's a pretty difficult thing to estimate in real life, so we don't know for sure if it would render the entire Earth uninhabitable. Life is pretty adaptable and our planet has went through some extinction level events before yet life persevered. Humans could probably figure out a way to survive, and regardless, it's still better to gamble on it than to put yourself at the mercy of those who want you dead.