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This topic has come up many times. I'll say it again, I don't like linked avatars, for a lot of reasons. I've asked on other sites the opposite question.
A proper avatar is <1k and not a bandwidth issue. In fact it makes a site appear faster when you're not making 20 external calls just to show a tiny picture(s). Not to mention that many or most of these linked avatars are much larger than they should be. Doesn't matter if they are resized, you still download the whole thing.
It is very easy to upload an avatar. If the user has one they like they can grab it and upload to their profile.
Hint: signatures do allow links. Users can put their junk there.
Idea: for linked avatars it might be nice if it worked like headlines, the server does the grabbing instead of each browser. The link and image gets cached at the server. The server then sizes the image for efficient delivery.
Fun: turn off external images and browse a site. Some sites use a lot of external content. I'm on some boards that typically run many times faster this way. No more silly animated avatars and flash and whatnot. But the relevent content is still there which is really what I want.