The way it started wasn’t that you had to pay it off every month, but rather that you have to pre-pay.
American Express’s foray into financial services started as money orders and traveler’s checks. The idea behind a traveler check was to keep you from having to carry large amounts of cash. If lost or stolen, they could be replaced. They could be cashed in at nearly any bank, and many businesses would accept them as well.
They were very useful before the advent of credit cards being more or less universally accepted.
At a certain point, they started offering a card that did much the same thing, but, like a traveler’s check, had to be pre-paid.
They do still offer traveler’s checks, but I don’t know why anyone would actually get one anymore. Last time I saw one was the late 90’s, and that was quite the rarity.
They still do.
Back in the 80’s, a business had to take a carbon copy of your card, and then actually send it in to the credit card company, then wait for them to send back a check.
Amex may have just been slower at processing, or may have lower priorities towards small businesses like a bus service in a ski resort.
Today, funds can be deposited the same day as the charge is made. Many still don’t take Amex, as they do have a higher processing fee.