It would be useful if there was an option in the “Change your profile picture” window in profile preferences that allows one to chose their minecraft character as a profile picture.
There are services (for example Cravatar.eu or Minotar.net) that would provide the images.
You can do this already 
When you click “Change avatar”, you can select an option to upload your own. In the resulting explorer window, simply paste the direct url to your image (for example http://cravatar.eu/avatar/lemodile/600.png) into the selection bar and press enter. That file will be used.
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Ok lol. I thought this was only for local files