> This is to ensure that customers always ask for receipts, so that stores always enter everything into the register (which goes into the store's tax filing).

It's fairly easy for a store to use a register that has nothing to do with the store's tax filing.

Receipt matching would defeat that, but only if stores submitted their receipts.

However, you can use customer receipts to estimate a store's revenue, but that has nothing to do with whether or not a register is involved.