It makes a whole lot more sense from a testing and EMF perspective. A connector is generally much more predictable than wireless- and the user interface is a lot easier to understand and troubleshoot by an everyday person. Getting bluetooth to pair or setting a phone into a hotspot and then joining the device to the wifi network would be a support call nightmare.

I think it makes infinitely more sense to give you something you plug in. Attackers can't hijack the signal in interesting ways, and nearly anyone who would use a Square device would be familiar with how to plug things into a 3.5mm jack.

The new Square reader which supports contact-less payments uses Bluetooth - so they're moving in the right direction at least.