This was my first thought when I read the summary as well. S/MIME is even built into the default mail app in iOS... not sure about Android (or any of its manufacturer variants).
The biggest problem with S/MIME is managing the certificates. People generally won't want to deal with having a different private key on every device they use for their email... especially when you consider that doing so would require the sender to sign with the correct public key for the device the recipient wants to read it from. Not gonna happen. So you need to have a private key that can be securely copied to every device the user checks email on.
And, of course, the second biggest problem is webmail. Though I have no doubt if S/MIME were to really take off there would be an API for decrypting message in a browser window while keeping the private key private. It would make it impossible to read messages on some random computer... but then again, putting your password into a random computer isn't really a good idea anyway