>If things go south really really bad, we can just get the private key and sign certificates by hand.
Very clearly states that someone has access to the CA cert's private key outside the context of the automated signing service, and can use it to manually sign certs for users if the CA service is down. So the CA service can be bypassed if it goes down,.
My point is that you cannot eliminate all dependencies. And if I must have dependencies, I'd rather put my trust in a well-engineered, time-tested, highly-available system. When properly implemented, LDAP + SSSD is such a system.
At any rate, an even faster and more reliable emergency response system would be to place a static user ID and password in a lockbox (virtual or physical) somewhere and use that to log in. You don't need a complex CA infrastructure to attain that; NSS fallbacks to static /etc files would suffice.