I agree with Andrew’s comments.
In my experience with other banks (and really any large corporate), they won’t want to offer incentives to everyone, because then they will end up paying out all of the people who would have stayed regardless. If you call up to cancel, they’ll pass you to the team that deal with cancellations, whose job it is to “save” you as a customer, and they will be authorised to offer you the incentives you seek. It could be a waiving of the annual fee, a one off point bonus, whatever. But the key is you won’t be offered it until you’ve shown you’re prepared to walk.
Personally I don’t think this card was worth the annual fee before the AMEX changes. Once you do eventually get off this card and leave for something else, I would suggest an AMEX issued card, not a bank one, for the same reasons as Andrew, and also the bonus spend categories.