Some people do not have the rights to online privacy. For example, when accessing a website from the library of a jail. The authorities want and need to know what you do, this for some obvious and understandable reasons. I agree this is a particular case, but this is still a case for allowing a website (as long as this is anonymous usage of it) to be available without SSL.
Does it work with sites like Google from Google Chrome where browser knows about their public keys? I think that this will be wide practice in modern browsers.
HSTS/HPKP headers could be stripped by proxy but preloaded public key list probably will require custom browser build.
