The kind of people who ran coupon schemes in the pre-internet days could have told you this. Back in the day, coupon schemes were things like you had to physically cut out and mail in vouchers from newspapers or magazines, and you got a discount on something like groceries in return. The point of this was market segmentation: you want to get people who (1) otherwise wouldn't buy your product, or at least not as much…
You just split the entire world of coupon users in 2 arbitrary sections. That's another value judgment.
There are many other reasons to use coupons. Such as: I like a good deal. I like to use coupons. I wanna try something new. I am bored and want to cut coupons. I got this coupon book. This place opened and I'm not sure I wanna try it full price. Etc.
There are so many ways to explore this question.
As for "worse customers", it is entirely possible for a customer to be bad, and for it to have nothing to do with being poor. I recommend studying the user journeys of user cohorts motivated by external rewards, vs those who aren't.