The big question is - who is Square competing with.
Now that Square is a public company with shareholders, the Silicon Valley mantra of growth-at-all-costs no longer generally applies, instead the focus is on profitability/ROI. Which is something that Square lacks, and is in an industry with slim margins already.
Anecdotally, tons of other people. Looking at the coffee shops and smaller stores in my area there's a pretty wide array of iPad-POS systems in use that aren't Square. In fact where I am (NYC) I'd wager that Square holds a plurality of that market rather than the majority.
Most of their frontends (in so far as I have to interact with them as a customer) aren't quite as slick as Square's, but they do get the job done, and presumably vendors use them because they're cheaper, which only underscores how fragile Square's business is.
These third party solutions aren't as sexy or slick as Square, but ultimately when it comes to payment processing sexiness is very, very far down the list of priorities.
It's also worth noting that there are big juggernauts moving in on Square's territory of physical transactions - PayPal being one - who already run enormous electronic payment volume. Stripe also has a big piece of the electronic payments pie and can potentially move in on Square's territory, while Square has so far been unable to branch out beyond physical payments.
This reminds me of Peter Thiel's thoughts on monopolies.
Square are in competition with every payment method of every kind. They are not in some tiny "niche" category of payment that will somehow remain invulnerable to competition from banks, Apple Pay, Android Pay, Stripe, etc. etc.
I don't see how they can possibly survive in the long-term.
I'm sure you can build a great business in that market, but is it a 3 billion dollar business?
There's a bunch internationally where Square hasn't really begun to compete.