The question comes before the restaurant. People search for what the format is, how long it takes and what it costs, and the place that explains it clearly is the one they book when curiosity turns into a plan.
The fixed price is the first filter. A counter meal competes with a theatre ticket and a long dinner elsewhere, so the number has to be visible while somebody is still deciding what kind of evening to have.
Occasions carry the decision. An anniversary, a birthday or an evening to impress somebody is what justifies a fixed-price counter meal, and pages written for those occasions reach people with a date already chosen.
Enthusiasts search for the chef. People who travel for meals want to know where the chef trained, which fish they work with and how the counter is run and who tell everybody where they went.