What are your calculations? Square, Stripe et al are making massive margins on debit card transactions right now. Thanks to recent regulations (the Durbin amendment), the average debit interchange fee is 0.89% all included.[1] Square charges 2.75%. That means they're netting around 1.5-2% on debit transactions. That's huge for a payment processor.

Sure, they have higher costs for credit cards, and their easier sign-up probably means more losses from seller-side fraud. But if they can control fraud then 2.75% is still a healthy gross margin even on credit transactions. And it's crazy big margin for debit.

[1] http://www.federalreserve.gov/paymentsystems/regii-average-i...