In my opinion, QKD (implemented correctly) performs key exchange, basically like Diffie-Hellman except that it’s secure even against an adversary with unlimited computing power. If I had a quantum computer and a quantum network anyway, may I’d use it, but probably not with Wegman-Carter. If not, I wouldn’t.
(BB84 is from 1984. The terminology was different, and the understanding of what mattered in cryptography was different.)
BB84 (and QKD overall) requires authenticated channels. You have to get those somewhere. You can get them from an information-theoretically secure MAC, but it has significant downsides. You can get them with computationally secure primitives, but then there's no point in using QKD in the first place. You cannot instantiate QKD securely without one of those two choices though.