The answer is not privacy-preserving for any sense of the word "privacy" that includes non-disclosure of a user's phone number as a legitimate privacy interest. Your threat model is valid for you, but it is not universal.
The question you posed, how Signal's identifier system minimizes metadata, has a clear answer. I'm not interested in comparative threat modeling, but rather addressing the specific objection you raised. I believe we've now disposed of it.
I don't believe there has been any such disposition in this thread. There have been vague assertions that it's been asked and answered elsewhere. Meanwhile, the Signal source code, and experience with the software, clearly demonstrates that a phone number is required to be proven for registration, and is persisted server-side for anti-spam, account recovery, and (as of a few months ago, optional) contact discovery purposes.
