Isn't this essentially a rudimentary implementation of what a credit card already does?
Using your example, the bank that issues the CC is acting like a CA would - linking you to a real identity. The bank is acting as your escrow (ok... not in absolute terms, but kinda), ie you are spending the banks money first which will guarantee the transaction, however you ultimately pay the bank back.
Well the bank has to identify you every tx. In reality they don't. who asks for ID when you are buying $100 or less of goods? In my use case there would be possibly 3 ways for a customer to establish credibility with the merchant:
1) Use an IRL ID (drivers license, ssn, whatever) submitted to a 3rd party who then establishes you as a trusted BitNote issuer. You don't ever even have to send the private key to the 3rd party. Just the public key. Your Bitnote uses the Privkey to sign the Bitcoin privkey, which is a statement that you, a verified real person printed that bill. In my use case the bill is scanned and discarded so that they btc is immediately transferred to the vendor. But because you are a verified person with a public key on file with the 3rd party, which is checked instantly by a query, the vendor takes a now small risk that you are 2x spend attacking. If your BitBills were go bad, the 3rd party would place a blemish on record.
2) Place an escrow amount anonymously with a 3rd party in exchange for listing your pubkey. If the vendor gets screwed the 3rd party can keep the cash himself (soas there is no incentive for the merchant to cry wolf). So long as the merchant doesn't doesn't trust you for much more than you have on file he should be fine. the 3rd party can sign the escrow address proving instantly to the merchant they have bitcoin on hold associated with that public Bitnote signing key. (i think the btc protocal even allows for 2x signing and all kinds of escrow stuff thats not in the white paper(
3) Publish a public key on some free server and everytime a merchant accepts your notes and they are valid they sign it, building your rep. So maybe merchants would keep you to small amounts till you build up the rep. All possible anonymously as well.
Your theory is sound, however the problem that always stands, is the dependency on a third party - and trust. This is also where problems tend to occur as there is a conflict of interest between the security and storage of your personal information and anonymity.
Again, i laid out methods where you can use it with total anonymity, or just use your real name with a 3rd party. but the merchant wont' know what personal info is on file with the 3rd party, only that your bitcoin privkey was signed by the person who established the account with the 3rd party, and some belief that the 3rd party does a basic level of policing to make sure you can't create multiple throw away accounts.
This method would seem to be better than the ease of identity theft today anyhow. The 3rd party never sees the privkey. In fact i dont' know why it is when we go to take out a car loan, mortgage or credit card we don't have to sign the application with a personal key. Might stop a good chunk of identity theft.
Lastly, this would be for casual transactions. No one will hand over the keys to their car in exchange for BitNotes without waiting for some confirms, and no one has to. Large txs of all kinds using whatever currency need time and usually paperwork to go through.