If a restaurant runs on a 9% net margin and pays around 3% in card fees, then roughly one-third of its net profit is going toward payment processing.

It's weird how this works. Saw something similar when working for a bus company. After reaching a minimum amount of sales for a bus route, everything after that is basically pure profit. However, how do we get those last sales? Well, by bidding higher on people searching for transfer between those two cities. Let's say the ticket was $20. We could end up for instance accepting to bid $10 for an ad that would lead to a sale. So for every $10 of pure profit we then got, Google also got $10. In a sense it was a good deal for both parties, but it's also kinda insane that in the end, Google made as much profit on our busses as we did.

If they're running on 9% net margin, then card fees are pretty down on the list of problems. They're vulnerable to any kind of fluctuation.

Yes, restaurants in general are vulnerable to any kind of fluctuation.