To give you a somewhat constructive answer... My non status dad was flying on miles to Europe, and has a delta Amex. He was able to check one bag for free (for intl). The Amex fee waiver only applies to domestic flights.

As for the cost of the flight, I don't believe there is a differential or a connection with how much you pay and how many bags you can take. (unless you book j)

Solution: he checked a regular suitcase and carried on a roll aboard. I flew over a month later for a long weekend, took home his roll aboard, and he checked his one luggage and had a decent size carryon. (I did this during the dmqm promotion for pit, so it was purely selfish on my part)