> Credit cards are cheaper than cash for most merchants.

Huh. I always thought it was the opposite. I know several restaurants that refuse to accept credit cards. They are great places to eat, but I won't go there. I don't think they miss my custom, though. Refusing to accept credit seems to be a signal of excellence, around here.

In Belgium it is common knowledge that cash-only places don't report everything to the feds.

For the same reason those food establishments had to get a government approved White Cash Register, because there was so much money disappearing.

If you don't do the accounting, it appears that the fees on a credit card are greater than the cost of cash and so restaurants that haven't done their accounting closely often think they're getting themselves something by not accepting credit cards.

The cost of a credit card is very obvious. The cost of cash is many small things that are very hard to see and thus very hard to account for correctly.