Not true. If you get any kind of refund on your Wells Fargo credit card, and you want to move it to your checking account, they send you a check by snail mail, which you then deposit. If you use Bill Pay to a recipient that isn't one of the few companies they have electronic clearing with, they make you enter a physical address, for... right, mailing them the check. There is no universal system advertised by the banks I've been with to send money electronically between consumers. If I want to pay my homeowners association's dues (which, coincidentally, I am in charge of, too) I have to use a check. All the above thus includes two scenarios where I essentially end up sending a paper check to myself. I'm European import to the USA, so I may not have figured it all out, but boy, I tried.

Edit: Forgot about this one: good luck being a foreigner paying the USA government for your immigration proceedings... right, all paper...