I can understand your feelings of unfairness. I too feel that the system can sometimes cause good answers to be inappropriately and unfairly buried at the bottom.
In practice, I occasionally use a workaround when the situation you described happens: if I'm confident my revised answer is correct and truly excellent, I might delete my original flawed answer, and then post a new answer with the correct information. Be cautious, and be sparing about doing this. This could easily be viewed as an abuse of the system if done indiscriminately. If you find yourself doing this more than once a year or so, I suggest carefully considering whether it is possible that you could be more careful before posting answers to ensure that your first post is correct. So in my opinion, this should be a last resort. That said, the benefit this has is that it doesn't require any changes to the Stack Exchange software.
Regarding your specific proposal, the issue seems nuanced, with reasonable arguments on both sides. The existence of a problem doesn't necessarily imply the system should be changed, or that every proposal to fix it is a good idea. One has to evaluate the potential for unintended side effects of any change to the system. Automatic notifications of the sort you describe have the potential to become annoying, and it is possible they might influence the incentives causing people to be less careful in composing their answers, so it is debateable whether your proposal would be better or worse. That requires careful analysis, and haven't done that analysis, so I have no position about that.
Changes to the system would require changes to the software, which would affect behavior across the entire network. Consequently, this is something that would need to be implemented by Stack Exchange the company, and they would have to be persuaded that it is a beneficial change for the entire network. So, this would need to be discussed on the SE-wide Meta, not on the Math Meta.
And if we check the SE-wide Meta, it turns out that this idea has been proposed before by many others. The idea of allowing people to notify downvoters, or of edits automatically notifying downvoters, has been considered extensively, and rejected by the company and/or the community because of the problems doing so would create. See, e.g., Allow an edit to notify downvoters: "I think I've fixed the issue now - please check", Please re-consider allowing edits to notify downvoters, @Downvoter sends a notification to all downvoters for your post. I suggest reviewing those requests and voting on them.
It seems possible that the current system is better than any plausible alternative for "fixing" this unfairness. Every system has some weaknesses, and whenever we consider any solution to a problem, we have to evaluate whether it might cause new problems that are worse than where we currently are.