Suppose you knit mittens and sell them for cash out of your garage. The IRS expects you to report and pay taxes on the income. How do they check that the sum you specified is correct?

Not sure how it works in the US. In Germany you are supposed to have a cash register or issue an invoice on each purchase, and sometimes (though really rarely given lack of personnel) they can randomly check of your reported numbers make sense together.

It's not clear how that sort of thing would even help, it seems like just a trap for the unwary. If you're an honest person selling your mittens and paying your taxes without knowing you're supposed to have a cash register, you could get unlucky and get in trouble for innocuous behavior. If you're a drug dealer then you get a cash register and ring up all your drug sales as mitten sales. Or, if someone wanted to report less income, they would have a cash register and then use it to ring up less than all of the sales. Whether or not you have the cash register can't distinguish these and is correspondingly pointless.