> You can get them with computationally secure primitives, but then there's no point in using QKD in the first place.

I don’t entirely agree. You can build a computationally secure authenticated channel using symmetric primitives (e.g. hashes) that are very, very likely to survive for a long time. And you can build comparably secure asymmetric authentication schemes from the same primitives (hash-based signatures are a thing).

But to build a classical key exchange system, you need more exotic primitives (Diffie-Hellman or public-key encryption / KEM schemes), and the primitives of this sort that are supposedly post-quantum secure have not been studied for nearly as long and have much more structure that might make them attackable.

Not to mention that attacking the authenticated channel in QKD cannot give a store-now-decrypt-later attack.