2021 Update: Just marked this as status-deferred. We will consider this request as part of a larger inquiry into abuse and how to mitigate it. This is not on our roadmap in the near future.
2018 Answer:
We're going to consider this.
This didn't make as much sense in 2009 as it does today mostly because in 2009, people came here for the rules; they were fed up with other platforms where the noise far outweighed the signal and at that time a little abrasiveness, even when kinda obsessive, was a price most were okay with paying for high signal with very little noise or distraction. I think even I said 'get a thick skin' back then and that was one of the wrongest things I think I ever said given what I've learned since then.
Putting something like this in place back then kind of felt like giving in before we figured out how far forward we could push without it. Twitter dog piles back then weren't very common, nor was people cycling through dozens of bogus accounts to deliberately target and harass people, which is unfortunately something that keeps the community growth team busy.
We're going to take a look at this through (what I fear) is going to be rather painful analysis and look at all of the ways where the option to mute interactions in a more granular way might make a bit more sense. The goal here: Let people turn off specific kinds of noise at certain thresholds, but don't hide abuse that we really need to be dealing with at a lower level by simply burying it.
We also don't want new users just cramming their fingers in their ears, which could be tempting if they get off on the wrong foot. Changes here have to fit in closely with changes to help users post better questions to begin with.
I don't have an ETA but as we look at ways that we can make people more confident that they have some control over what rings the inbox notifier, it could serve as a last stop above the current level of toxicity that some have been reporting.
And before you go nuts, I said consider
When / if we roll this out it will be much more considered than "just build a per-user mute button". We have to look at other aspects of the software that lead some folks to believe that 'mutable' behavior is acceptable if you're a good enough rule lawyer, and put our 'be nice' policy more in front of people as a solid code of conduct with advertised and consistent consequences.
So, yeah - we have to keep up with the times, and maybe we waited a little too long in this (and other) areas of the site to finally accept that there are social aspects where we need to be much more influential, if not in complete control.
We're going to take a look, and there will be a separate (2018 version) discussion once we've got some ideas.
Thanks for poking this.