I don't think any "role" per se is "bad" to take up (of course, unless it's the role of the dominator etc.) I think why some people tell you to avoid being timekeeper is because often people fight to keep time, but the person who ends up keeping the time doesn't participate as much in the actual group discussion because they're so focused on the timekeeping.
So if you can keep an eye on the time whilst still being an active participant, I don't think being timekeeper is bad. It is only when that thing becomes your only role is when I would advise against it. And of course, if you take responsibility for something, you have to see it through. If you volunteer as timekeeper but forget to inform everyone there are only 5 mins left...not a great look lol.
So in the true lawyerly fashion: the answer is, it depends.
