Storing the avatar on the blockchain is out of the question.
Perhaps storing an URL of the avatar could be done ONLY if a significant fee in BTS is burned.
To avoid scams we can use a fast name visual similarity check. It should verify that each new account name is not similar to previously registered one.
If newly registered account name is similar to previously registered one => the new account cannot publish avatar unless that right is bought from the old account.
This is way over-engineered. We need a simpler product, not going down rabbitholes like this.
Any publishing of pictures is bad. So you put a URL of the logo of a competitor and don't even try to have a similar name. People can not be allowed to put in images, it just opens up more social based attack vectors. The feature isn't needed if it requires extra features to counter-act the damage it does.
If there was open-sourced data with images + textual names they could be pulled into one big picture with something like imagemagic and then just extracted using canvas features in javascript. It gives an image that #1 doesn't look like it is trying to be a person/have a personality (whatever it is that people see as 'unprofessional'. It also works better than the robots as far as being able to remember them.