When you pay with a one-click checkout process on Amazon or purchase songs on iTunes, nowhere are you asked anything about your "wallet". All you did was leave your card details with these retailers to simplify the checkout process. Customers would be confused to hear about an iTunes "wallet".
The payment industry needed a name for the thing, and came up with "wallet".
It's very funny how our brains work. As soon as we gave it this name, we started thinking about emulating leather wallets and instantly began moving towards irrelevance.
What would have happened if we had called it "opening a tab" or some other such thing?
I have a similar issue with the word "loyalty program", a metaphor for volume based discounts. In every single conference on loyalty, people get caught up debating the concept. You can almost always hear someone say, "If you want loyalty, get a dog" or some other similar remark.
So much energy goes into the metaphors that we choose. The metaphors truly structure the way we think, making it very difficult to think outside the box.
This is a great opportunity for innovators looking for stress lines where they can create disruption. When you see lots of people blindly following a metaphor, go back to the original idea and find pain points that are not being addressed. They are there. Nobody else will be looking for them, because they will all be busy replicating things like leather wallets in the sky.