This is the real reason why cryptography hasn't caught on. It's opt-in by nature - No matter how hard you try, you can't send someone an encrypted message if they don't have a public key for you to use.
Actually, yes you can. Check out identity-based encryption and Voltage Security. It's currently in use by Wells Fargo, ADP, and other large enterprise customers.
The catch there is that IBE requires a centralized, trusted key-issuing service where you need to enroll to receive your message. If that's compromised, then game over.
Of course, you would need to be judicious about which group of key issuers you are willing to trust, but this method will at least reduce the risk. The other nice thing about this is that even if some key issuing service is compromised, the sender can force the receiver to switch services (compare to the TLS model, where dropping a CA is basically a coordination game problem).
