Another explanation is that McDonald's wants to use this to price discriminate - to separate customers. Readers are reminded that there is always a time cost to obtain McDonald's coupons, and they are not readily available - browsing on McDonald's website to find coupons, printing coupons, or reading McDonald's promotional newspapers, or asking for them on the side of the road, all cost a small amount of money, mainly time. What kind of people are usually willing to spend these costs? It is the people who have cheaper time costs. Of the people who can go to McDonald's, what kind of people have cheaper time? Obviously it's some people on the lower end of the income scale - the working class.
Also, what coupons are able to purchase is usually some specified combination of items, not random purchases. That is, there is a cost to the customer who uses the coupon - the cost of not being able to pick and choose items at will. That's also a cost.
In short, there is a price to be paid for using coupons - and a price is a cost.
By all of the above, McDonald's has succeeded in separating the rich from the poor among McDonald's customers, and then, for the rich - those who don't hold coupons, McDonald's supplies them with more expensive goods (no discounts), and for the poor - those who -coupon holders, McDonald's gives them a discount. The time and place goods are the same but the price is different, this is typical price discrimination. By price discrimination, McDonald's extracts more consumer surplus from consumers and increases profits.
How to verify the above theoretical explanation?
First of all, we need to start from the above theoretical explanation to introduce a verifiable implication: according to the above theoretical explanation, the poor people should consume less while the rich people consume more, so the total amount of consumption of those who get coupons must be lower, while those who don't get coupons must buy more and more expensive things. This is clearly an observable implication.
Second, observe whether the facts are consistent with the introduced observable implication. This step is not difficult: you just have to find a good spot and watch McDonald's sales carefully to see if the validation results are consistent with the theory's conjecture.