Personally I haven't tried Google Pay yet, but I foresee a future where I will be able to check out at a store by simply waving my phone over the payment terminal, and it knows which account I wish to pay with and if I'm a member of the store's rewards program.
Long gone will be the days of shuffling through your wallet to find the right cards to pay with. At least that is what I believe is the ultimate goal of Google and Apple in regards to their payment apps.
I can see this as a possibility with the way technology is moving forward towards smartphones being an all in one device for storing and transmitting your information.
Although making it easier to complete point-of-sale transactions is nice, the better selling point can be security as many banks and retailers have suffered data breaches in recent years.