Apple’s current business philosophy (since Jobs’ second tenure) is based on delighting the customer with disruptive, bold moves that make life better.
Customers would see moving to Apple as an alternative to (and initially in addition to) using their traditional credit card. It would be more convenient for those with Apple iPhones; it would at least cost no more, but the main advantage to the user would be a guarantee that information about the user’s life would remain the property of the user. It would be stored and shared only in the case that he/she explicitly decided to trade it for some benefit, whether to Apple or some other party. The consequences of this would be made clear to the user.
(Presumably, Apple would perform some analysis on your usage patterns to be able to flag possible fraud. All of my credit card providers do this and it is a welcome service.)
Apple would make it clear that they would comply with any legal constraints and requests by law enforcement agencies, but the contrast with Google and Amazon would be stark — and those are the real competition to Apple at present. I strongly believe that soon there will be a revelation that will expose what the sales-centric life-trackers (which also includes Facebook and soon Twitter) actually do and how they use it against you.
If many people knew what I do about their assault on privacy, there would be a mass uprising against these companies. Apple could fill the void. In fact, I cannot think of any other company with sufficient goodwill to do so.
Naturally, Apple will be in a fragile position on this and will have to be more transparent than they currently are. The recent flap about tracking software on cellphones (including in a limited way, iPhones) affected Apple more than anyone else; presumably, everyoneexpects Google, the carriers and HTC/Samsung to be scuzzy.
Other Innovations
There are areas where Apple can innovate in the banking business beyond transaction management, though transaction management by itself could be huge.
One of Apple’s problems is that they generate a lot of overseas profit that is expensive to repatriate. This geographically distributed capital could allow a micropayment system across national boundaries with no currency conversion fee. Those two elements are rarely found by themselves and never together.
Apple could pioneer in per-use software micropayments. They are already trending toward this already with the App Store, where 99 cent applications are common. Five years ago this would be considered micropayments. What if you could download any app for free and only pay so much according to how much you use it? What if you could subscribe to quality news websites for a tenth of a cent per article read? Or TeeVee shows?
What if you could trade your automated toll payment system for an iPhone?
What if you could participate as a microlender?
What if you wanted to go the other way and sell your personal information, cutting out Google? Suppose you could be paid a nickel for every targeted, geolocated ad you agreed to consider?
Disruption in the very fluid of the economy, and the most intimate value: privacy.