Having worked at a bank for a year I can certainly say, banks need the federal government just as much as the federal government needs the banks. The federal government (as well as state governments) frequently use banks as a low cost, low risk way to increase access to capital for those that need it, as well as of course controlling interest rates to then control the speed that the economy grows or shrinks

A well-regulated private banking industry allows the competing interests of a government and a private company to compliment eachother in ways that really only become apparent from directly working in the industry. The government provides grants and subsidies to allow small banks to provide access to capital that might not otherwise exist, competition with other banks forces banks to provide better services to customers and government regulations prevent banks from taking too much risk or doing too much harm, plus a strong government safetynet protecting bank customers from failure all come together to provide a surprisingly good system. I'm not saying private banks are perfect nor that its the best system one could dream up, but in a society that relies on capitalism as a method to limit access to resources, a well regulated private banking industry with strong competition (which we actually largely have!) is really good for consumers