There may be thousands of banks, but all but a few manage their funds at one of the big few, essentially acting as resellers of the big banks' services. For example, I my bank is "Ally Bank", but if I ask them for instructions on how to receive a wire transfer, they instruct me to direct it to "JP Morgan Chase Bank, N.A.", the largest bank in the U.S. I previously used the brand "Simple Bank", which provided accounts via "The Bancorp Bank", the 5th largest.

It's a similar case to cell phone providers: although there are hundreds in the U.S., all but four do not operate their own network, but rather resell the network of one of the big four.

It's an interesting question, though, how much this consolidation is due to regulation versus being a result of a natural monopoly, i.e. high barrier to entry for the type of business.