HIPAA requires any email with patient data be encrypted. That kills any attempt to receive email on a smart phone.
Nothing about a smartphone prevents email from being encrypted. The fact that nobody's sending encrypted email does, but that's a user adoption problem rather than a technical problem. The technical problem is solved, solved well, and has been solved for decades.
The world needs something like iMessage but more open.
We've had the ability to do this for a long time, but only a few major players are in a position to ensure sufficient user adoption, and they're not interested in creating anything that doesn't drive users to their walled gardens.