This feature isn't available. But what I should be able to do is create a new them with no avatars. That's now on my list of things to do.
I've created a new theme, called 'reduced images', it contains no avatars when you're reading posts, and also doesn't have the fox head image at the top. You can select it at the bottom left of the page. Click where it currently says 'Default Style' and it will give you the option to change it.