Originally Posted by
steve4
I found it easier to cancel cards right before the annual fees were billed because although it was rare, sometimes it took me more than one phone call to have the fees reversed, likely due to inexperienced reps, but who knows. I just don’t want any hassles

How so? You can cancel the card by automatic robot call, dont even need a human being.
Never have fee not automatically reversed the next day in my memory.
The goal is to stay on the safe side so you would not accidentally trip the wire to be labeled being abuser on AMEX's terms.