Chrome does check that all certs (at least [the ones issued after April 30][1]) are recorded in a Certificate Transparency log. Or rather, it checks that multiple logs have promised to include the certificate (via a signed certificate timestamp); the code that actually queries the CT monitors to verify that the certificate was included [isn't finished yet][2].
Browsers don't and can't check CAA records, because that's not how CAA is supposed to work. CAA is only enforced at the time of issuance. If you temporarily switch your CAA records to allow issuance for an hour, issue a cert, then switch them back to block all issuance from all CAs, the cert you issued remains valid.
Browsers don't and can't check CAA records, because that's not how CAA is supposed to work. CAA is only enforced at the time of issuance. If you temporarily switch your CAA records to allow issuance for an hour, issue a cert, then switch them back to block all issuance from all CAs, the cert you issued remains valid.
[1]: https://groups.google.com/a/chromium.org/forum/#!msg/ct-poli...
[2]: https://bugs.chromium.org/p/chromium/issues/detail?id=506227