It may be a bit confusing, but is it really necessary for users to be able to choose their own time zone? I can't think of any practical benefits to this, nor any situation in which you would ever need it. It would be nice, maybe, but certainly not necessary.
As it is, I'm pretty sure that timestamps are used mainly only in situations where two similar answers have been posted- then, others can see which answer was posted first (in cases of significant overlap). There's no issue in calculating this using the times in UTC, as the comparison is equally doable. Plus, most interactions with posts happen within the first 24 hours of their being posted, and it's during that time that (instead of a date/time), it just says asked/answered x hours/minutes ago
or asked/answered yesterday
.
And, there are at least two problems that I can think of here: the rep-leagues and the rep-cap. If each user's week, month, or year starts at a different time, there'd obviously be an inconsistency. And what would un-logged-in users see when they visit the 'top users' page?
As for the rep-cap, that's even stickier. I may have hit the rep-cap
by getting 250 rep in the UTC day, but maybe I only got 190 in Central time. And, users could change their time zone to game the system: they could set a time zone where they don't lose rep from the cap, or they could set a time where they do hit the cap (for progress towards the Legendary/Epic/Mortarboard badges).
The only other thing that would be affected by subjective time zones are the Enthusiast/Fanatic badges, but even those aren't going to change that much. The point of those, as @Grace Note explains, isn't about the metric itself.
That's what makes it a Fanatic. It's not just for someone who simply pops in once a day for 100 days straight. The people who are in the best shape to earn this badge are the people who visit the site repeatedly throughout the day. People who are interested in seeing what's going on at the site, and perhaps shooting for participation as well. People who don't even have to watch the days tick by to try for this badge. The point isn't to tell people to just pop in once per day - it's to get people invested in wanting to know how the site is growing, and what is happening.
So there would be no actual advantage to the change, as far as I can tell.