Signal has spam issues even with the phone number requirement, as I've experienced lately (though nothing on the scale of Twitter). I dread to think what the spam would be like without the requirement of a phone number.
At least now you can solve the existing spam problem if you want by disallowing people from using your number to message you in the privacy settings and randomizing your username after anyone new adds you - that way your username is like a one time password to add you, kind of like what lots of people here wish existed for phone calls.