Similarly, Sam's Club does, or at least used to, take only Discover.
My wife and I have a few different credit cards from different companies, and all offer 5% cash back on a rotating calendar. Sometimes, Discover runs 5% cash back on fuel and Visa runs 5% cash back on groceries. Other times, Discover might run 5% cash back on home improvement stores while Visa runs 5% cash back on fuel. We have the calendars for each of our cards printed out and on our bulletin board on our way out the door of the house, so we make sure to use whichever card benefits us the most for whatever purchase we're about to make.
Stores that accept only one card crimp our style a little bit there, because we may not be able to use the card we want to use. In the end, purchases at warehouse clubs amount to a small percentage of our monthly purchases anyway...