In my experience, a lot of people who work in large companies who have authorization to spend decent money do. They can often get hold of a Visa or Mastercard instead but it seems to be more hassle to get authorized by a higher-up.

Personally, I have an Amex too and I'm not rich or special but maybe it's different in the UK. I use it because I get a ton of airmiles and Amex never seems to get rejected or stopped for fraud checking purposes.