The number of people is part of the phrase. Somebody organising for ten or twelve types that figure, and a restaurant that says which tables and rooms take which numbers appears for a search almost nobody writes for.
Occasions are planned rather than stumbled into. A birthday, an anniversary or a leaving dinner is decided days ahead by one person acting for a group, and that person is looking for certainty rather than the cheapest plate.
A per-head set menu answers the organiser's actual question. Somebody arranging a work dinner needs a figure they can put in a message to eight colleagues, and a restaurant that publishes one removes every reason to keep looking.
None of it works without a readable menu. Published as text it can be found for the dishes it contains; published as an image it is invisible to everything, which is the commonest technical failure in the sector.