Signal could still validate the phone number via SMS and immediately discard it afterwards.

Personally I liked the way ICQ did it back in the day, they used a uniq ID just for their service decoupling it from a phone number.

If Signal wanted to avoid long numbers, they could use a CorrectBatteryHorseStaple approach which is what Xbox does for their usernames if you don't pick one.

Easier to remember,