I don't think such a feature would have any actual benefit, for most cases there are sufficient notification mechanisms already:
when answer is accepted
This only concerns two people, the one accepting and the one who's answer was accepted. The first one knows (by default) and the second one is notified when he receives the awarded rep.
when some other person comments
If people want to notify you of their comments (in posts not your own), they can use the
@username format. If not, why should you be notified?
when the person asking the question comments
If that person wants to notify you, (s)he can either use the
@username format or comment in your answer. If not, why should you be notified?
when some other person answers
Again, what's the point? You are supposed to provide good answers anyway, you shouldn't care for competing answers. If you are interested in seeing what other people answer, you can always favorite the question and get notifications of updates.
when a user's answer is downvoted
If you are the one being downvoted, you get sufficient notification via the rep reduction. If you want to know when other people are getting downvoted, you'll have to explain what's the point (other than curiosity).
StackExchange sites are supposed to be Q&A sites. For any feature to be implemented, it must be valuable to the Q&A aspect of the sites first. If it only enhances people's social experience, without adding any value to the Q&A process, I don't think the developers should spent any of their time to it.