I did two times hackathons organized by Square, and have seen how their hardware is used in practice in Tokyo. Square targets payments systems and everything around that (like ways to manage through their APIs things like invoices, customers, employees, bookings, inventories, orders, etc). Square also sells POS which look a bit like macbooks in the past (white unicolor).

So from that, I guess Bitcoin could be a good back end to minimize cost when managing payments. Since it is international i believe there is a high cost of entry to do payment systems legally. At the moment as far as I have seen their API doesn't use Bitcoin since it can only generate payment links to pay through Google pay or Apple pay I believe, but I would not be surprise if Lightning invoices are integrated in the future.

I don't know if there is anything hidden since I almost never listened to Jack Dorsey directly, but from what I know of his company I would say Bitcoin fits his business model even though I didn't see Bitcoin transactions yet integrated in the Square API.