Another fundamental problem: SSL is only as secure as the private key of the certificate key pair.
So the CA certifies that the private key was known to some entity at some time. If the key gets compromised (without revocation), too bad. The certificate is now worthless. Even worse, now it creates a false sense of security.
How many sysdmins will take the trouble to create a new certificate after a site was broken into, and also revoke the old certificate?