The problem is the private cert.
It needs to be available locally on the client that encrypts the mail. In case of the a webmail app the private cert would be hosted on the server running roundcube.
That is the obstacle they have not overcome. Alternatives are not there yet. I hope the Roundcube Team will make some progress in this direction. There is some chatter in the dev mailinglist. You can subscribe on the roundcube homepage.