It wouldn’t surprise me if they do. Lets say I get $100 bill out of the ATM, if the government wanted to track that bill. They would need to find that bill again and then try to back track the route the bill took to me. A very time intensive task and ultimately could lead to a dead end. After all how many people keep track of the serial numbers of your large bills?
Compare that to a card. Literally everything about it is tracked, it is all done automatically and can be acquired from the bank.