Why/ why not? I don't because I think people are getting to know me by my whale avatar lol Plus, it helps people remember someone by their name AND the image they select.
Flipside, I can also see how people like changing it up to match their moods, the seasons, etc.
I have different ones for different sites, but once I don't ever change it from what I upload. People tend to identify me with my avatar because I never post pictures of myself, and so if that's how they best remember me, then so be it 🙂
I just use the same avatar for all site's that I'm on since I have that image for pick-up-and-go. I might have an odd avatar on some sites over the years. I do not change it enough