Depends where you are (like most of these things.) Where I've lived, card-only isn't uncommon because cash is an expensive hassle for smaller businesses to deal with. Also a potential security risk if it has to be left on-premise overnight.

However, this doesn't necessarily mean credit card, usually it means Maestro or EFTPOS or whatever. These tend to have low fees and function roughly like a near-enough-to-immediate direct credit.

In general, places that don't accept cash will also accept credit card for non-locals, but it's not at all uncommon for (usually smaller) places that accept cash to not accept credit card, even if they do accept the local debit card system, due to the extra expense.

And yet some restaurants in NYC still tried to go cashless. There are real benefits: faster transactions (no change) so faster queues during lunch rush, no risk of robbery, no need for armored vans to transport cash, employee theft becomes much less of a concern.

I think the benefits are compelling. NYC ruled it was a discriminatory practice though, because not everyone has access to banking/credit.

Or you pay the restaurant through direct bank transaction. Credit cards are needlessly expensive, but not all electronic payment systems are.