What if someone gave you change in cash, then you went to deposit it at a bank, and they refused to take it because those bills were in a registry? You could c

What if someone gave you change in cash, then you went to deposit it at a bank, and they refused to take it because those bills were in a registry? You could check the registry yourself before accepting change, but what if those bills weren't in the registry when you checked? Such a system could be implemented for bitcoin but there are crypto currencies with stronger privacy guarantees for which this would be practically impossible (those guarantees could maybe be cracked in the future, people are working hard on both sides).