The new exchange would add massive counterparty risk in my opinion which is the major incentive for using bitcoin.
Essentially you are correct, but this would all happen automatically under the hood of the merchant API. The end user need not understand that they are buying a promissory note, or transferring it along with their bitcoin via the API. All they need to have is an account with the exchange and some fiat funds.
I get that there is counterparty risk involved, but by making the system transparent and posting realtime statistics, trust could be slowly established. There could not be more guarantee-credits available than there is fiat funds to back them up. Merchants would cash them in immediately. They do not need to exist for very long. As long as both the reserve total and total guarantee credits issued is published in realtime, this will help negate the risk.
But we would only have the exchanges word that they weren't issuing more credit notes it would be impossible to check, and as the value of the note plus the bitcoin would (if everything worked) never change relative to the dollar (providing the change in bitcoin price wasn't greater than the value of the note) you might just as well hold usd which is far more liquid and by definition is less risky.
The fact that the bitcoin price might overrun the note could also be a problem because as the volatility rose the risk associated with this special currency would rise making it beneficial to the purchaser of the currency to ask for more to cancel the risk premium involved. This would mean the value of the currency could fluctuate especially if rumours came out about the exchange itself.
With pure bitcoins the risks are real but visible and observable, with this the risk is still there but harder to quantify and measure as it lies within the exchange and the volatility in the bitcoin itself.