I think the sad truth is that not only is encryption inconvenient for most emails from most users. It is just not even necessary. So, you are trying to decrease convenience for...?
It is worse in the web world. I want someone to be able to index my emails. As I do actually search on them rather often.
Unless there is a homomorphic technology I'm not aware of (very possible) to allow searching over encrypted emails, then I don't know how you can get around the fact that there is a third party that has access to the unencrypted. Once that happens, game is over. Right?