Now I believe everyone can agree that if this were a real bank and the bank stock has a non-0 value that each and every transaction would be valid and 'safe'. The USD note's from the bank would have a market value of about 1 USD and the purchasing power would be defended by the bank which would honor its IOUs. There should be no doubt that the USD would track real USD even though the bank never had any USD on deposit, only offsetting ledger entries and collateralized loans.
If I have $100 (or an asset unconditionally and irreversibly pegged to 100$), what's the point of putting $100 as collateral in the bank to get $50 as a loan and pay interest on it?