This opinion piece in the Motley Fool comparing Square and Visa made some interesting points. First and foremost it estimates that consumers globally still spent over $17 trillion with cash and cheques last year. That right there is the opportunity.
The other interesting point was that no one really wants to compete with Visa and the other payments processors. A company like Square has its own role in the transaction processing chain but still leverages off Visa's network. The same applies to Apple Pay and Paypal.
These companies want to play a role in the chain and make things more convenient, but no one is interested in taking on the actual switching process. VisaNet can handle 65 000 transactions a second and is one of the most trusted brands in the world. Visa has returned 810% in the last ten years; we plan on remaining loyal shareholders for decades to come.