For large financial institutions, they move money in different and less expensive ways. For example, ACH fees are a tiny fraction of the cost that you use when you move money by credit card, and they're almost frighteningly easy to initiate (there is 0 authorization for these). It's just rare for the banks to expose a way to do ACH for you except in the specific case of billpay (and even then, many institutions handle these as mailed checks rather than ACH).
The idea that finance has to be hard with big ceremony in order to be secure is a clever ruse by big banks. They're not content with the large amount of security-from-competion that regulation gives them. They want your trust, and they're not afraid to scare you into believing that they're the only option.