For large bills that is true to some extent, but having worked closely with secret service in the past at multiple points, they have confirmed my suspicion that $20s and below are virtually impossible to track and they do not bother unless they are specifically giving you marked bills because you are already suspected of a crime.
Also avoiding tracking by a governments and tracking by surveillance capitalism are very different threat models.
Getting down to 0 tracking is of course impossible, but the less data we leak the less clear of a picture third parties get on how to predict and manipulate our behavior. Why help them?