Their flat rate of 2.75% is substantially more than what Visa charges for "card present" transactions. The highest cost cards are 2.4% but they're going to be a small portion of most stores' card mix. I'd think most shops cost Square 1.1-1.5% across all their transactions. Debit volume exceeds credit volume in the US -- most people are swiping their bank check cards, not commercial purchasing cards and the highest end reward cards that require pristine credit -- and the Durbin amendment capped the interchange fee on debit cards (when swiped a-la-Square Reader) at 0.05%+$0.21 per transaction. That means 2.75% is 98% profit for Square on a big debit card swipe.
https://usa.visa.com/dam/VCOM/download/merchants/Visa-USA-In...
The only place Square's subsidizing the transaction fees is on very small purchases where the flat ~$0.15 of the interchange fee amounts to more than 1-2% of the total transaction, and with AmEx where, if Square hasn't negotiated better than sticker rate, they could be paying 2.85-3.5% depending on business type.
If they're losing money on the one thing they charge money for, what's the business? And how are their competitors doing it? PayPal's historically offered merchants with volume as low as 1.9%. They offer 2.7% flat rate (no per-transaction flat fee either) for their swiper.