I've just cancelled my Amex Plat after 7 years. It's not an easy thing to do so (not to mentioned the admin on my side to change/remove the automatic payments that go onto my AC card).
I was on the phone for over 30 minutes with someone (kind) gentleman trying to talk me out of it, but I was pretty set in stone on cancelling. It's also not so easy to just drop down to a green card (while I figure out what to do with my remaining MR points).
I've also cancelled my Business Charge Cards, but this has to be done by letter and the agent did advise me that no matter what I wrote on the letter someone would call me to talk me out of it because I am considered a high spender on my personal card(s) (> £150,000 per year).