I'd add that the 80x15 standard size for web badges wasn't supposed to substitute 88x31 web buttons, they simply ran more commonly in blogware while 88x31 was more of an "actual" webpage thing. For the rest, totally agreeing with the origins not having an exact reason and spreading easily becoming standards overnight. If we think about it these kinds of graphics have different preferred sizes depending on use, with fanlists being 50x50, Wikipedia user badges? I think they're called? Being rather big and then there's those very long and narrow "bumper stickers" designed to go in forum signatures.