No that’s not stupid. It adds a layer of friction for criminals.

True criminals do not care. Mafia do not write invoices to sell/buy drugs or to pay a killer.

Source: I used to be paid in cash (illegally) and it was a pain in the ass to do anything so now I get paid lawfully and my boss pays taxes

Then the problem was not that your boss was paying you in cash but that he had the possibility to pay you under the table without (basically) any kind of risk.