I haven't seen any high end restaurants that only accepted cash. There are a few inexpensive places here that are like that. I've eaten there. The food was good.
If I was hypothetically on the last day of a CC promo and 1 meal short of reaching a spend bonus, I would look for an alternative to spending $10-15 on "crap" food. If I couldn't find one, I'd buy the "crap" food. I probably wouldn't eat it though.
These days with Square virtually everywhere, I come across fewer and fewer cash only businesses.