Interestingly (sort of), 5%-or-$1 wouldn't work out well for Apple. This is because credit card processing fees are generally structured as a flat fee plus a percentage of the transaction.
Something like 5 cents + 1.3% would be a great deal on payment processing, generally. Apple is a behemoth, so let's assume they're getting a good deal.
For a $1 purchase that'd be ~$0.07 to the transaction processor... which is more than the flat percentage already. Then Apple has some amount of costs involved (bandwidth, maintenance of systems, general overhead, etc) even if they started running the App Store at cost as they originally claimed they'd do.
There's definitely room to lower the cut Apple takes... it's just that somewhere in the 10-20% range is still a reasonable fee to cover their costs.
It's also worth considering how gift cards affect what Apple can charge. Apple sells gift cards through retailers, who are getting a cut of those sales. That cut comes directly out of Apple's portion of the sale, so they have to account for some percentage of transactions having that effective cost, which is probably higher than the aforementioned payment-processing cost. (There are some markets where gift cards are incredibly common. Kids get given them a lot. They're super common in Japan and other countries for everyone.)
(The flat $1 fee wouldn't fall apart on processing costs until you reached really expensive in-app purchases... but it'd massively change the economics of the App Store, where $1 apps / in-app purchases are pretty common. I have no idea if that's a good idea or not.)