I'm always mystified why we haven't leveraged DNS.
I mean: why not have cookie policy set by a flag in DNS? Not unlike DKIM or even SSHFP.
Of course, we wouldn't need the entire certificate industry if we simply looked up a site's PK along with its DNS record...
You're talking about DAME (which email uses). It has it's own issues like not having transparency logs, and if a DNSSEC signing keyholder goes rogue, there is no easy way to revoke trust (unlike CRLs for Web PKI).