That assumes that notes spent at a store are kept and never reused; that’s simply not true. If you buy a €5 coffee with a €5 note and then later in the day someone buys a €3 muffin with a €10 note, your €5 note is given to them as change. Repeat that process in a town or city and that cash gets pretty shuffled quite quickly.
Your scenario doesn’t also take into account till “float” where a portion of cash is kept in the till/store/elsewhere to seed the till the next morning for the first customers of the day, should they need change for their purchases.
Pinchflat is way less complicated than TubeArchivist and integrated with Plex without any extra work.