Sure, all this sounds great, IF the students actually get taught this. I suspect many students do not get taught this to the degree you state and teachers in classes other than English Composition just do not have the time to teach this and thus depend on such checkers.
Is it lazy? Sure, but it is easy to say "there really is no substitution for care and attention to rules, details, and ethics’ when you are teaching it. Not so easy when teachers are in a school where these skills are not taught.