What are you talking about? Those who control your avatar's data outside of Nostr obviously have full control of it, but they can't be fixed. Within Nostr, your avatar's data is within your power to completely control. Have a local machine that runs a Nostr relay and content hosting, and the data you create is completely under your control.
Discussion
Do you run your own relay? Do you expect every user to run it? Do you know there are 5 relays everyone uses (thats why nostr “works” today) 5 more with some data but less popular. And 400 unused empty relays?
You can post your “avatar” to twitter/instagram/facebook and copy it immediately to your personal website, then you don’t need nostr, right?