An avatar is like a signature or a seal, and you are "signing" your profile with an avatar. Especially since you are using the same "signature" or seal everywhere. That's totally legit, according to me. If your avatar functions as your recognition device, so be it. I use my picture for LinkedIn but my avatar for all other activity on the Internet.
Back in the Middle Ages, your avatar would have been your heraldric emblem, which you would put on your shield so that others would recognize you, as you using your uncovered face as a recognition device would have been a very bad idea on a battlefield where every single sharp object would have an affinity for your face :)
The advantage of using an avatar is that your avatar doesn't need to change over the years as time catches up to you :) Whereas those who use a photo of their faces would have to update it every five to ten years - on every profile that they put out. Look at it this way, if your face got rearranged in an auto accident, you'd have to update your photos from a "before the event" photo to an "after the event" photo :)
On the other hand, if you are young, good looking and physically fit, why not flaunt it? You are always free to switch to an avatar as you feel the years adding up:)