It is possible to track the serials, if they wanted to; however, except for banks, I have not exchanged cash with a retailer who scans the bills at the point of transaction and if they did, they'd also have to tie a given ser no with me at the time of purchase. Since a particular bill will go through many hands, it'd be like trying to figure out who made a change on a system when it was done by 'root' or 'administrator' where the whole team logs in as root or admin. Basically attribution would be kinda inaccurate.
Something like half of the supermarkets in Denmark scan all money bills they receive supposedly with the purpose of defeating counterfeit money. However it could easily do OCR on the serial as well. Combine that with CCTV records, and and it does not offer much more privacy than credit card payments.
Ironically I started to appreciate it, after I received a fake bill from a different store.
They'll build a "better" cash register which bundles counterfeit money detector and serial number scanner in the same package. Combined with facial recognition on the cameras and accurate timestamps on both CCTV and the cash register, you have your perfect money tracking system right there.
No they won't it would be too high cost, it's easier to make it very convenient to use your phone or card for payments and 95% of people will follow suit.
