Earlier quoted context omitted.
It's not about using a ledger to hold public keys. The keys exist regardless of the ledger. The idea is to use the ledger to indisputably prove ownership or control over resources. Could be money, could be access to certain services, could be files, anything. Also, the ledger doesn't have to be public.
If the ledger is not public, why would I trust it? If someone else claims they are you, how would I differentiate the conflicting claims?
This is how JWTs and many other protocols ensure message authenticity.