I wonder if no checks includes no debit cards. That’s about all I use these days, but I don’t eat in restaurants very often.
On the rare occasions that I order pizza I always use cash. It’s never even occurred to me to use a check.
But I would never use a credit card for something as trivial as pizza.
The paper check is an awkward thing compared to the debit card, which can be treated as if it was a credit card if the merchant desires. Not enough money in account comes back as though it were credit limit reached, so in either case the merchant (and customer) are warned.
However, I’d be hesitant to use a debit card as a credit card if it had to be “run” out of my view, like some restaurants do. Some employees aren’t honest and will copy your card for future fraudulent use.