That's the worst-case-scenario guidance. Bank of America will print and mail a check if it can't find an electronic method. I have a client who sends me his monthly payment this way.
If you're sending to a known entity like the electric company or a credit card, it's immediate.
As you, yourself noted, "I haven't interacted with American bill payment infrastructure."
Perhaps reserve your comments for things you know about.
I didn't comment; I asked a question. You are upset that I asked whether bill payments are instant?