No-one has or would suggest that avatars are more important than the text content; but individualising authors can add authority where deserved. The argument about identity theft, if serious, was specious.
So long as members were told not to use copyrighted images, and mods removed any challenged avatar (or any 'reported' internally), then the legal issue is overinflated.
I don't deny that many avatars are 'stolen', but that fact is not a valid argument against their use ("you can't drive your car on this road, because many drivers have broken the law on this stretch").
The only argument against so far with anysubstance is the suggestion that there may be more work for the mods; that I cannot deny, but I think it will be pretty small - most serious offenders will be losing whole posts or membership, rather than a simple avatar.
Avatars really don't need defending in the 21st century, and demolishing paper tigers is a sacred duty for those who see them for what they are.
The positive benefits are that many members like them, they do no measurable harm, and those that don't can choose not to see them. Just like the ubiquitous ;)