Search suits a small part of what a restaurant sells
Most dining decisions happen in maps, in social feeds and by recommendation rather than through a search advertisement.
Somebody deciding where to eat tonight is usually browsing a map, scrolling a feed or asking a person. Search ads reach a fraction of that, at a moment when the searcher is comparing everything within a short drive.
The intent is also thin. Generic terms about food near a location produce clicks from people who will pick whichever place looks best, and being the ad rather than the top organic result is not a strong advantage there.
That does not make paid useless. It makes it selective, and the selection matters more here than the bidding does.
Where it works is where the search is deliberate: catering, private events, large parties, a cuisine somebody has decided on, or your own name.
Being honest about this matters because restaurant margins are thin. A budget spent on the wrong part of the funnel is money a restaurant cannot spare, and the alternative uses of that money are frequently better.