Easy 10
Brain dead MUG SHEEP
Thing is, if I'm being responsible then I will report my covid status accurately so there is no need for a photo ID. And if I'm being irresponsible then I will fake my covid status and the photo ID will just corroborate the faked information. So it doesn't seem that the photo ID is useful in the cases of either the responsible or irresponsible people.
I think the overriding point is that the vast (VAST) majority of people attending aren't going to be there jibbing the system. Is it still possible ? Yes. Nothing is entirely foolproof.
If you are not a dickhead though, then you can return to the Amex without any of the ADDITIONAL tricky hoops of trying to trick your way through the system. So the photo ID is useful, in that it will filter out the vast majority of pricks who would descend on the Amex if it was just basically a free-for-all with no checks.
I don't really understand what else you want the club to do. Other than just throw the doors open, with no checks whatsoever ? In which case - that would probably put me off going.