Signal doesn't ask for phone numbers simply to combat spam; the phone number isn't an elaborate captcha. Rather, as this article repeatedly points out, Signal doesn't keep your contact lists and other data available to its servers. It uses phone numbers because phones already have contact lists, stored clientside, keyed by those numbers.

To replace the numbers with usernames, Signal users would have to either give up contact lists altogether (at which point nobody would use the service), or allow Signal to keep a serverside database of contacts ready at all times for users who log in. This is what other messaging services do, and the result is that the servers have a plaintext log of who talks to who on their service, which is the most valuable information a secure messaging service can make available to a state-level adversary.