When I was a young man, back before the dawn of time when dinosaurs roamed the Earth and Americans weren't afraid of Muslims, I had a wallet full of gasoline credit cards. Union 76, Shell, Texaco, Exxon, Chevron, Mobil...all in the name of being able to buy gas at whatever gas station happened to be convenient.
Then the oil companies got with the program and joined the 20th century, and started to accept Visa, Mastercard, and others. Now I've replaced the stack of proprietary credit cards in my wallet with a single card that I can use anywhere. It's better.
Unfortunately, as we enter the era of contactless payments and smartphone apps, not everyone wants to accept Apple Pay or Android Pay/Google Wallet. So now, when I want to buy aspirin at CVS (or shirts at Walmart), I have to download and install their proprietary app and register my credit card, or else pull out my physical wallet and pay cash (or use a plastic card).
That's not particularly difficult, but it does negate the biggest advantage of using Apple Pay or the equivalent: security.
You see, it's not just a convenience thing. When you pay with Apple Pay (or equivalent), the merchant never sees your actual card number. Apple generates a special number that only works with your phone. Anyone who was a victim of the Target hack will appreciate the importance of this.
Meanwhile, if you're using the CVS app or the Walmart Pay app, you don't have that advantage. The merchant gets your actual card number and keeps it on file. If they're hacked, you're screwed.
So no, Walmart and CVS, I won't be using your special proprietary payment apps. Maybe they make it easier for you to track purchases, or maybe you've negotiated a special lower per-transaction fee with the banks. I could certainly understand how it might work to your advantage. But neither of those is a compelling reason for me to downgrade my own security.
And one last thing to keep in mind: The consumer still has choices. You both have competitors who will accept Apple Pay, and they'll be the ones getting my business.
And if/when you reconsider your policy, so will I.