FWIW another datapoint, I called up to cancel my platinum charge today with AF due in Feb. I cited the EK/SQ devaluations, as well as a bad experience I had with their travel insurance medical assistance. I've only been a customer for 12 months, and don't spend a huge amount, so wasn't expecting a terribly high offer.
I was offered 30k points to stay, the agent was quick to offer it and I only mentioned the experience with the travel insurance benefit after that, but apparently it is an automated offer that they can't influence.
Kept the card anyway as I got slightly more than the AF in value last year excluding points, so the 30k points is (barely) enough to push it into the black for me. I do wonder if the offer would have changed had I called back in 2 weeks, but I guess I'll never know!