What if one of your physical paper currencies in your wallet right now was involved in a robbery at some point? Should that serial number no longer be valid and

What if one of your physical paper currencies in your wallet right now was involved in a robbery at some point? Should that serial number no longer be valid and cause you to lose that money when you attempt to spend it in the store? If currency is successfully laundered it frequently will end up in someone elses wallet - the same would happen with bitcoins, with the main difference being that it could be tracked back to the originating offense. Maybe an exchange will want to keep an eye out for that - but what makes you think a laundering site or gambling site will care? I give you $100, and you give me back $95 from your wallet and since I can use a different wallet to receive the funds it isn't tied together. In the end someone will end up with those hot bitcoins and fractions there-of, but they might be completely innocent - so should they not be able to use those funds? Should every person care about the source of their money? If you could track your paper currency back, would you reject any transactions that were at some point involved with some illicit behavior? I'm not talking about the technical feasibility, but really if people are bothered enough to care.