Unfortunately, there isn't a ubiquitous enough system for a lot of messages that should be secure. Like password reset links, financial and medical documents, vulnerability disclosures, etc.
Besides the fact that no encrypted messaging system is sufficiently ubiquitous, Signal is not a great fit for these things because it is tied to a phone number (what would be the equivalent of security@mycompany.example? What if you don't want to give out your phone number, or your phone number changes?) And it is optimized for mobile messaging, and while there is a desktop app it isn't a great experience, and Signal strongly discourages third party clients.
And I do love Signal, I just don't think it can really fully replace email. And I don't know of anything else that is well positioned to do so either, though I would love to learn of something.