People will want receipts on site. For day-to-day transactions, it looks like a hassle but I could see this being great for paying back friends or whatever.
EDIT: Then again...I can see where wanting a receipt could be valid--to make sure you're not getting ripped off. Makes me think of the sign next to registers in most fast food joints: "Call 1-800-whatever if you didn't receive a receipt and get a free order of fries." I'd still go receiptless, though, for places I know to be absolutely legit.
Receipts are up there with cashiers giving me a bag for a single item I can easily carry.
(I'd be very surprised if the main use of Squareup was "paying back friends".)