A set of CAA records describes only current grants of authority to
issue certificates for the corresponding DNS domain name. Since
certificates are valid for a period of time, it is possible that a
certificate that is not conformant with the CAA records currently
published was conformant with the CAA records published at the time
that the certificate was issued. Relying Parties MUST NOT use CAA
records as part of certificate validation.But with DANE TLSA Resource Records you can pin a public key to a website. Alas the implementation of TLSA-RR checking in browsers is dependent on extensions at this time. I wish it was native in browsers with a big red sign when violated. When done in combination with DNSSEC it's very hard to fake certificates. Or more precisely asymmetric cryptography key pairs used by servers. Certificates for TLS would not be needed anymore if TLSA-RR's were standard practice. A company might still use a certificate to attest it's identity beyond internet domain ownership.
Edit: This is for TLSA 3 1 1 and 3 1 2 records. That's what I have experience with. Just read on Wikipedia a lot more is possible with TLSA-RR's including certificate and CA pinning. https://en.wikipedia.org/wiki/DNS-based_Authentication_of_Na...
When a CA can be shown to have misissued a certificate, Google can (and has, as it did in the Symantec case) distrust it, nuking the CA from orbit. It has no such powers with a CA baked into the DNS; Google can't distrust .COM. People should be careful what they wish for.
But not too careful in this case; DNSSEC is moribund, and unlikely to be revived.