The price would be too high - Apple has never paid more than a few hundred million for any acquisition[1] and Square are reputed to be north of $4B[2].
OK, but I still don't see a compelling business reason that having a payment processor would be good for Apple. They can already process payments, how does helping Barbara at the flea market of Little Jim's Cafe process credit cards help their core businesses?
That sounds more like the "Apple should own everything" school of thought. More like what Google or (old) Microsoft does. It doesn't sound Apple-y.
They actually already do this with their retail stores: You can scan products with the Apple Store App and pay for it using your Apple ID and its charged to your credit card on file.
This is brilliant when you're at a mega-busy Apple store on a Saturday afternoon and all you want is a Lightning cable adapter. Pick, scan, pay, show the nice man on the way out, PROFIT.
