As a diamond, the best experience I've ever had, was checking into JFK 23 minutes before the actual flight time.
My luggage was delayed coming in from Jet Blue. I had somewhat anticipated this and had called into Marco Polo HK about 40 minutes before flight time, asking them to help and try to hold the seat as long as possible, and that I will show up in "10 minutes". When I did I ran directly to the first CX agent. They said no way to check in. I mentioned that I called before and that I'm diamond if it helps the situation at all. And she took my stuff and checked me and a colleague in immediately, escorted us through the gates and we were on the plane. I don't think they would've done this for a Gold member. They have all my 200k miles in business a year.