A blockchain seems like a very reasonable way to provide a distributed immutable log of actions that take place within a PKI infrastructure. It even adds the ability for 3rd party auditors to participate in the system in a real-time manner.
You might even extend it, so that instead of it being PKI with a blockchain transport, to something more akin to Kerberos with a blockchain transport -- every attempt, successful or not, to access a resource could be immutably logged, and access could be granted by the targeted resource only once the authorization message has been committed to the blockchain (and therefore approved by auditors)