[simiones]

> What allows you to say that they have different identities?

Syntactic analogy with non-zero sized types. If you want a special case that says "there is a single object of the zero-sized type" that's ok, but it's a special case. All other types have a difference between object identity and value equality.

> Will all addresses be equal?

No, because C++ doesn't optimize for ZSTs, and it doesn't modify semantics for const. I agree that C++ pays a price for these two things, but I don't think it's because it "insists all objects have different addresses", I believe that is just a consequence to not giving special semantics to const beyond disallowing writes.