I can't say I speak for Square and I definitely don't know the details of their contacts with the credit card processors, but 2.75% is probably limited by what they get charged to process the credit cards. I would hazard a guess that they got between 2 and 2.5% and are skimming the other .25 - .75% off the top for themselves.
My father in law runs a small business and has shopped around for credit card processing in the past. He has a deal around 2% at the moment. If you are diligent about shopping around and being part of merchant groups and such, 2-2.5% is doable. If you are not diligent, a business will probably get 2.5-3% per transaction. If the business is huge (national chains) with lots of negotiating leverage, they can do even better. Mind you, this number off the top of my head are ballparked from anecdotal experience.
My guess is Square negotiated a percentage when they started. They have since proven their business and are processing enough transactions that they were able to renegotiate a better deal. Then they passed on the savings. I am sure they would like to drop to 1.75% if they could, they still have to pay the credit card processors and make some money. But that is all conjecture.