Nah, it gives people more pleasure of achieving their armatars that uploading random pictures. Also the moderator would be flooded with pictures that they would have to check if they are appropriate and who wants to do that all day long?
Here's a bonus of being able to upload your own pictures: flash avatars. There is only one forum that I know of that does this, and that is the DarwinBots forum (search on Google if you need know more...) This would let people upload small games as their avatars. Small enough games take less space than jpegs or PNGs. As for achievements, you could let people upload larger (dimensions) avatars or something. Or maybe you can only upload your own picture when you have enough APs? As for inappropriate avatars, people should be able to report it AND be able to hide that user's avatar. Yes a mod would be flooded with avatars to check. Maybe try to split it into, say 25 pictures per person and ask some users to help? (I would be willing to help, I'd be happy to check, maybe, 1000 pictures a day. That is if they were emailed to me or uploaded somewhere for me to download in a .zip file. It wouldn't take long to check 1000 pictures when they are all avatar-sized)
I personally don't much like the style of the Armatars.
You can not take everything cool and put it into one site. That disrupts the flow of the site.
AG takes pride in it's Armatars and although it would be cool to upload your own pictures, it would ruin the flow of the site. The AG Armartars are one of the few things that makes this site different from every other site so allowing people to post their pics would work, but would not be nearly as productive as using just the armartars.
Yes, it may work on other sites but this is not the "other sites". It is ArmorGames.