Notionally, I would imagine something that looks like "email" and acts like "e-mail" (to the end user) could eventually exist that provides the same (conceptual) security that the Signal protocol provides (and perhaps a hosting provider option that's the same level of user confidentiality that we get the Signal foundation), although you're correct that foundationally it would be a different protocol. Backwards-compatibility would be required, at least for seamless transition (perhaps represented as "secure" and "plaintext")
Wasn't Ladar Levison (the individual behind Lavabit) working on something like this? https://darkmail.info/