Automatically approved bills didn't get auto paid - but they appeared in the "upcoming bills" when issued, with a pay date of the due date on the bill. I could go an hit "pause" or "stop" on any bill - and it either wouldn't pay or would be removed entirely. Anything that wasn't auto-approved would start in paused mode and I'd have to manually approve it - but that was a single click.
Still, I agree that when I'm in the states it feels crazy old tech. They still require signatures on credit cards!