Yes, that is true as it grows. However, I thought that Square planned to make their systems ubiquitous and use that leverage to lower fees and pressure Visa to make changes to merchant guidelines and offerings that benefit Square's goals. Yes, this is speculation as I'm not involved, but Jack Dorsey has an expansive mind and the fact that his ambitions for Twitter included its current role in exacerbating political revolutions suggests he wants Square to have similar power in business.
The goal of a disruptive technology is to force the establishment to take smaller cuts to avoid losing market share, not to get them to agree to a fair exchange.
But how is 'more ubiquitous credit card processing' going to eat market share away from credit card companies unless Square starts issuing its own credit cards? At some point the gambit would have to be "I'm going to drop VISA and start issuing my own credit cards... or VISA can just take a smaller cut." That doesn't seem likely.
First, Square might avoid needing a traditional credit card with their products somehow. I realize mobile payments and other methods have been tried before but eventually it's going to work. This would have the effect that Craigslist and Ebay had on newspaper classifieds by reducing the market for VISA's products for banks and merchants.
Second, Square can definitely compete in the cardspace. What's impossible for them now could change with a big enough operation.
Third, Square can use their ubiquitousness to lower fee structure as has been said. That will reduce market share of the fees in the payments 'stack' only; VISA/MC will still exist everywhere. I think this will be necessary for them because their biggest competitor right now is cash, because they want to do every financial transaction in the world.
Since all of these 'disruptions' would probably boost the other I predict a combination from them from the company that gets as big as Square wants to be.
