I'm not sure of your assumption that lack of total anonymity implies no privacy. They are independently important concepts. You can have privacy (no knowledge of information shared) without anonymity.
The phone network can do that just by correlating traffic to devices, it doesn't need any help from the software running on those devices.
If the target use case was people that could reasonably do the job of limiting the information just the use of their devices leaked, it might matter. But the target use case is replacing SMS and the like, so it really doesn't matter (except that people want to pretend that the use case is something other than replacing SMS).
Of course there is. That's why one of the cleverest parts of signal is the engineering to invalidate number 2. Moxie and signal are the world leaders in trying to make it impossible for the service to know who you communicate with... Even to the point of using the Intel secure enclave to audit the server software and validate that it doesn't peek.
That's not the point. Why doesn't Signal provide the option of using a pseudonym? The model is broken from the perspective of people who care about privacy.
1) what's your number, and 2) with whom you connect or communicate.
That is, there's still the danger of social graph analysis: "Oh look, this person's communicating with a known journalist!"