This is a strange case for bitcoin, competing with credit cards. Most consumers would be better off paying with a card: same cost (none), more protections (the ability to dispute bad merchants over defective goods). It's not a bad idea for Square to add it, since some people have bitcoins obtained through speculation, mining, cheap money transfers, and so forth. But even so, they would be a little better served payin…
I think security would be an obvious answer.
Credit cards are like symmetric cryptography: there's only one secret (a number), which you must share with everyone you ever want to send or receive money from. Any malicious actor who gets that number can then use it to extract money from your card. Sure, it's probably FDIC insured, but they still make out with some of your money.
With Bitcoin, you only ever share your public key. It operates entirely on public key crypto. You can safely share your Bitcoin account public key with anyone and everyone to send and receive funds. Plus, anyone can verify any time you send or receive a payment very quickly. That way you can't lie and say you paid when you didn't (no checks in the mail). You also can't do chargebacks or otherwise recall your funds, like you can easily do to scam with credit cards or Paypal.