That thwarting is honestly trivial to counterthwart without even trying. The register at the coffee shop knows which note Alice paid with and which ones they gave in change.
If I buy coffee at Starbucks with a $5 bill, and you come in later, pay with a $20 and get my $5 in change, in order for the government to follow the money like that Starbucks would have to scan every bill and correlate the scans with individual transactions. Even if people were okay with that (which I doubt), it would be a costly imposition on businesses and a huge time waster for everyone.
Knows that a note Alice withdrew was received and what notes were exchanged. But not necessarily that it was Alice (though other data might corroborate that).
Alice can just withdraw a big note and break it up by buying a coffee, then use the change from that transaction to buy the drugs instead.
Granted, some extra creativity would be required for drug purchases involving large amounts of cash