That sounds absolutely horrendous. Even Whatsapp allows you to verify using a fixed line and claim that number on the mobile for privacy.
Coupled with the recent LocationSmart revelations, it would make Signal unusable for those who wish to keep their location private. You absolutely need to provide the mobile number of the actual terminal being used.
I needed to give them a phone number I could read SMS from to set it up, but there's no need for that to be "the mobile number of the actual terminal being used".
At least on iOS, apps cannot get the phone number of the device through any APIs in the iOS SDK (AFAIK). So no app on the platform can reliably confirm if the number you entered is the number of the device. They all assume that to be true when you confirm the code they send by SMS. As another reply here has put it, you just need a device to receive the code via SMS. You can then use that code on any other device to set it up.
Coupled with the recent LocationSmart revelations, it would make Signal unusable for those who wish to keep their location private. You absolutely need to provide the mobile number of the actual terminal being used.