If someone edits your post, it appears under the "Responses" activity stream on your profile, but doesn't trigger an inbox notification. Should it? I for one would like to know if someone's editing something I wrote, without having to check my profile all the time. I know edits are generally minor and done in good faith, but sometimes they have the potential to unintentionally change the author's intent/meaning.
I'm not generally in favor of aggressive edit notifications because I think it leads directly to edit wars.
Most edits we see are quite small and it is extraordinarily rare for an edit to cause issues as you describe.
And as you noted, you can periodically check your profile to see what edits have occurred on your posts, and take action as you see fit.