The most interesting thing about being in China is seeing how 99% of merchants power their business with a Wechat/Alipay QR code printed on a piece of paper. Not sure how Square missed that.
QR codes have been available for a while. Square helped do payments through credit cards. At that time payment via QR codes was cumbersome, and not adopted. But I think it depends more on the consumers and local economy. US was anyway using credit cards a lot. Asia preferred cash, for smaller transactions.
You can pay credit cards with QA codes. You just don't need the POS device.
I think US as a whole is behind using QR codes for payments in general. One big reason is banks. The credit card culture of US made it almost impossible for new technologies to come and break the ground. Till this day there are banks who issue credit cards without chip and people prefer to use it.