Yea Kerberos is another option. If you have all the necessary pieces, that is... you’d need managed devices, an LDAP/AD setup, DNSSEC & SSHFP, PAM & various agents on servers.
Certificates offer all the same benefits, and a few more, with less work & fewer moving pieces. They’re also more flexible since you can control the auth flow to get a cert.
You need GSSAPI anyhow if you have Kerberized home directories and not typing passwords at ssh. Although you're likely to have LDAP (in which you can store public keys), all you need is the KDC and a simple Kerberos setup on ssh clients and servers. I wonder why anyone thinks you need more.
Kerberos tickets and infrastructure are roughly equivalent to using ephemeral certificates as far as I can see. The one reason you might want certificates is if you require FIDO MFA, as I don't know if you can use anything other than OTP with Kerberos implementations. (The hook for "the auth flow" is preauth.)
You can also use "GSSAPIKeyExchange yes" to solve the trust-on-first-use issue without resorting to DNSSEC, since the server identity gets verified via Kerberos in that case.
The main benefits of certificates I can see are the increased auth flow options and better scaling at large scales since you lose the service ticket traffic.
Also, I'm not convinced that TOFU for SSH is really all that terrible. Maybe it's just my use case and my situation, but I SSH to the same servers over and over again. And if I need to give access to someone new I give them the public key first.
SSH X.509 looks like a complex solution to a not very big problem that can be more easily solved with DNSSEC and SSHFP.
* They put authentication to your SSH servers entirely under your own control, without escrowing keys to the operators of the TLDs.
* They're deployable independently, without enrolling all of the rest of your infrastructure into DNSSEC and all its unreliability and complexity.
* They integrate with IDPs, so that users can get short-duration authenticators based on MFA logins, without storing long-lived secrets on their machines.
SSH X.509 certificates have nothing to do with the web PKI, other than that they use the same encoding. Engineering orgs that use SSH CAs run their own CAs. That's the point.
Happy to have helped!