I’m of the opinion that “you pay if you invite” is based on two things.
The first is carrying over invitations to eat together before restaurants. Of course the host would make the food and not require you to bring your own. They pay for and make the food, so why not also pay at a restaurant?
The second is that going to a restaurant tended to be an affair of those who had money, and thus the imposition wasn’t high. They could easily have enough money to pay and it not be a budgetary issue. But, as restaurants became more the fare of the common man, it became more and more common to ask everyone to pay (set up in advance, of course, so not rude) and thus that became the norm.
That said, the OP’s question is different, and I’m not sure. If the coupon was just something like “half off” for everyone, then I would 100% expect them to let you use it, no question. You’d get one bill, and then split it between you. The more money you save, the better.
On the other hand, if it were something like “Get this meal free,” then I’d tend to think that whoever ate the meal gets the freebie. People generally pay for their own meals.
If it’s something more like “get $x off”, then I’m unsure. I would tend to think it would make more sense to combine the bill and give each person half of that off. But I also wouldn’t have a problem if they said “We have coupon for ourselves. Would you be able to join us?”–clearly setting up the expectation that they’ll use the coupon for themselves only.
Finally, if the coupon is one that’s easy to get, like from a newspaper or mailer or something, I’d expect them to help you get your own to use. You know, tell you where to get it and such–not saying they have to buy another newspaper for you.
I assume that’s not common for an expensive restaurant, but I could see them doing it to get people in if the restaurant is new or something. Or, you know, during a pandemic when they’re just trying to get people to come in. So it’s possible the OP is describing that sort of coupon.