Is it possible to remove badges if you do not want them? If not, is that something you would consider adding as a feature?
No, this is not possible. I doubt it will be implemented.
If you find it distracting you can hide them locally (others will still see them). For details see: How to disable/remove all badges and reputation? and https://stackapps.com/questions/3105/hide-all-pointless-user-data-gravatar-badges-and-reputation