Some of the posts above are too much.
The airlines are free to decide if they offer alcoholic drinks or not and how many.

That someone needs a drink to "relax" and tolerate the X hour flight is not a reason for the airline to be obligated to serve alcohol.
The airline is not obligated to accommodate the medical needs of an alcoholic with withdrawal symptoms either.

So, if AA decides that an F ticket allows ONE drink, they can do that if they wanted to.
Or if AA decides to go completely dry like Saudia Airlines, they could do it if they wanted to.
Not that any of the above necessarily makes business sense.

I myself may enjoy two or three glasses of wine on a 4hr+ flight if I am in F and I would not like to be limited to one as suggested.
I do think that the FA has to have some discretion of when to cut someone off.
It doesn't matter that "I was fine after two bottles of champagne"... Me saying "I am fine" can't be the criteria for the FA to cut me off, we are all always" fine" when drinking