In 2011, Brett King was promoting his book, “Breaking Banks,” and creating a start-up that he hoped would do to the banks what Amazon did to the retail industry and Facebook did to media. “We had grand ideas of being the Facebook of banking, and being a new form of bank account,” Mr. King said recently. Six years later, his company, Moven, has opened only 60,000 of those new bank accounts. Mr. King has now transitioned to selling his software to the banks he once scorned, who use it as a component of their mobile apps. “We realized that if you want millions of users as a bank, it is a very different proposition than building a social media network,” he said.