Cross-platform (Chrome web-apps don't count), Federated, Distributed, to name a few. The reason email is so entrenched is probably because of these reasons entirely. Being able to send a message from any provider to any provider certainly helped spread adoption easily.

There are protocol properties, and client properties. I think some of both are important.

### Protocol

* Easily federated

* Identifiers can be memorable/meaningful (unlike phone numbers) while still being globally unique (thanks to federation)

* Device independent (not tied to a phone number, can generally use the same account on different devices)

* Can contact people you don't know/haven't met (this is possible with Signal, but they'd have to publicly share their personal cell phone number, which is a no-go).

### Client

* Optimized for longer-form, less immediate messaging (folders, drafts, rich text)

* MIME attachments (Signal supports only a limited number of predefined types of attachments)

I feel like you could probably layer an email-equivalent on top of Matrix, but I'm not 100% sure about that.