If Square wants to be a cash intermediary, they should offer Monero. It's the most cash-like coin available since it's the only one that's fungible - an important aspect of any currency. The only problem is that it's not as recognized as Bitcoin, so maybe they're just trying to attract publicity and new users?

The ring signatures have a big scalability problem, and the cryptographoic strenght of the monero anonymity is all but proven. Monero is an interesting experiment but its feasibility as a long term store of value is to be provem.

Also, moving some transactions off-chain transaction will effectively mix the coins and strenght anonymity.