That still doesn't solve the question of identity. For example, I could generate a GPG key for 'Johnny Daniels' and sign a loan. Without some sort of way to validate some traceable information about this person, having a signed document doesn't really mean anything. Or am I missing something?
Reputation would not be on you, as a physical human being. It would be on the GPG public key.
Basically people will think "I know that the guy, whoever he is, who uses this GPG key has always paid his debts. So I guess I can trust him to pay this one."
If you lose your private key, then you'll lose the associated reputation and you'll have to start again with a new, zero reputation key.