Currently using the bill to replace cash means that you either need to have the exact amount or else cash would be needed as well to supplement the payment amount or cash would need to be given as change. With an exchange that floates, prices are probably not known until payment is made so the chances the buyer already has a paper bitcoin in the exact amount would be even more less-likely to occur.
I am looking at it more like a personal check. Once received, you hold it if you trust the person, or you deposit (redeem) it into your personal account.
Then throw the paper away.