Er, it is implemented in the client! S/MIME has been implemented by all non-webmail clients for years. When used correctly it's more or less transparent: every email is signed (you get an smime.p7s attachment), and if you receive a signed mail and have S/MIME configured too, your client can/will automatically encrypt the response.
But there are reasons it's not widely used: in the consumer space, most people don't bother getting an email address cert (even though Comodo and StartSSL give them away for free, it takes 2 minutes). And in the corporate space, often you don't actually want employees using end to end encryption, because you need the ability to do things like have internal messaging archives that are searchable, you need the ability to do document discovery when you get sued, employees suck at key management and keep losing them, etc.
Encrypted asynchronous messaging is just a tremendously hard problem. Look at agl's Pond project to get a flavor for what doing it seriously takes.