A quick and easy solution is to use some other system for authentication using discourse connect.
My earlier estimate of how hard it would be do create an email-free system is wildly off. Using some other identifier with a not-email.invalid hostname for those emails should be doable. I think that Sign-In with Ethereum plugin might do what you want, if you’re willing to make people use Ethereum, but something similar could also work. You do need some way to establish identity.