I'm not a huge fan of QKD, but there is a potential use case for it. Basically, for digital signatures we have schemes like SPHINCS+, and perhaps also PICNIC and FAEST, which don't require "mathematically structured" assumptions like other public-key crypto, but instead are secure based on not much more than one-way functions. If (and it's a big if) quantum computers can break all those structured assumptions but not AES/SHA, then we would still have secure public-key signatures, certificates etc but not KEMs.
But QKD can, in principle, securely distribute keys if you have a way to exchange quantum state (e.g. line-of-sight or some sort of currently-nonexistent quantum router) and a classical authenticated channel. SPHINCS+ could provide that authenticated channel. In that case QKD would enable secure key exchange even between parties who don't have a pre-shared secret.
Of course right now, all of that is science fiction.