I normally fly Delta, and have never had problems in entering their lounges as long as I presented my AMEX platinum card and had a boarding pass for a flight on Delta that day.Exactly!
To me that is a great benefit esp. when I am on vacation. Arrive at the airport at the recommended 2 hours before, if you get through TSA quickly, head to the Skymile lounge for a couple of "free" wines. In the bars in the terminal, this would be $28+ for me and my wife. Fly to Atlanta, where we repeat the Skymile lounge.
Return trip would be similar.
The $200 fee re-reimbursement which they started last year also is a plus. I am "old-school" where I don't want worry about how to pack all of my clothes into a carryon. I prefer to check in my suit cases and just worry about carrying on my camera/computer/electronic bag.
Base on the above scenario, I have already covered $300 of the platinum card's annual fee.
There is at least one intangibles.
In general the airline clubs can be a quiet respite from the "drone" of the main terminals and the airplanes themselves.
Each person needs to make their own cost/benefit judgement
Airline Lounge access is what caused me to get the Platinum Card in the first place. I was paying the same amount for an annual fee anyway so why not get the added benefits?