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 paying by card, due to the extra consumer protections they'd enjoy.
Where bitcoin makes more sense to me is in replacing cash. But that mostly makes sense to me in the real world where you can inspect goods and whatnot in advance of cash payments. (There's maybe some potential for it online in the form of micropayments, where trust and protections don't matter so much.)
But for online sellers that already accept cards, I have yet to hear why bitcoin reflects a better choice than cards for the consumer. Anonymity maybe? For the average consumer, not worth the tradeoff in lack of ripoff protection.
Sellers would be better off, sure, but don't forget it's a two-sided market and consumers are heavily incentivized to use cards. Most of those "high fees" are funneled back to the consumer's pocket in the form of benefits and rewards. It's a form of lock-in to the CC system.