They already process cards over the Internet with Square Marketplace. They clearly were interested in entering this area, but fell years behind everyone else despite having years+ first mover advantage.
I remember emailing Tristan O'Tierney back in 2012 asking about an API after having seen that they had allowed a small beta group access to an API [0,1]. His response was just that they'd decided against moving forward with it -- not sure of the specifics but they had at least gotten that ball rolling at one point before deciding to focus on other things, would be interesting to hear more about that decision.