It’s not anonymity focused.
If I want to have private conversations with friends, family or colleagues signal is fine.
We expect heads of state to be able to have “private” discussions while knowing the other heads of state they may be communicating with. I can have “private” conversations with my partner, even though people know who that is.
You can also choose to anonymously communicate with no privacy, Reddit or 4chan style...
They may not be totally orthogonal, but I don’t think either privacy nor anonymity are encapsulated by each other.
There is also still privacy in public communications when done anonymously, as you can't tie the information disclosed to the real identity (necessarily). -- Hence why for privacy purposes advertising data is often anonymized. (But again, less private of course, if ie I said I was a 2 fingered man in Poland and there is only 5 people fitting that description)
So I'd still say, perfect privacy cannot occur without anonymity.
Even if this 'hackability' is an issue only with the security of the phone/hardware - able to be hacked and thus reach the decrypted signal messages - That also means, that person's Signal contacts also have their real identities exposed. (Where they wouldn't be if the account names/ids could be arbitrary like eg. wickr)