Square is tackling different type of merchants. It's not quite this that is keeping Square from an IPO; but they messed up in a few ways along with Chase (their merchant acquirer) releasing the same product undercutting the Square margin. Not to mention PayPal's ability to lower the price or the international market is almost gone for Square (others have copied Square).
I hear you on that. I guess it depends how narrowly one defines market. And I guess the more narrowly one defines it, the harder it is to justify a valuation.
That being said, I suspect my downvotes were a function of Jack Dorsey fanboys knee-jerking more so that my overly broad definition of the payments market.
Actually, Stripe's market is smaller than Square's. But these business models will never capture a large percentage of their respective markets anyway due to the high rates (negotiating with an acquirer can get you almost 50% less than their rates). After all, "Simple Pricing" is not as good as it sounds. Why pay 2.9% on a 0.05% debit card for the sake of simplicity? I'm sure Excel can handle these variations. This is an unfortunate consequence of the inefficiencies of that industry.