Signal requires a phone number and does not want anonymous users, so I do not want it too.

so does Telegram

But Matrix does not. I wish they removed email requirement too though.

It depends on the matrix server, they don't have to require an email address per se.

The phone number is only required to create an account, and is never used again IIRC. The rationale for it was to prevent abuse/spam, but I believe there is now an option to purchase an account for a small fee without needing a phone number.

Purchase can be done only through Apple/Google Pay which require a phone number and a bank card on top of that. Do not be deceived by marketing people.

Yeah having to doxx yourself to avoid giving a phone number is a bit disappointing for a privacy-conscious messenger app.

Especially because they have their own crypto coin right there in the app so why not allow payments with that?

The Signal desktop app is complete and utter garbage.