I've thought about this some and one way to at least "sort of" map a private key to a single trusted real-world individual/entity is to require it always keep a balance of some "high" amount on it to be considered valid. So three banks start out signing some new "blockchain" ledger with their private keys, each with $100M on it, and they probably are going to be really careful with those keys from then on, and not let anybody who doesn't really represent the entity sign things with them?

I think this is the idea behind proof-of-stake. I don't see how it mitigates the fact that while the cryptography may be secure, the humans handling the keys are less so.