Very interesting comments on this subject and it seems to be a concern for a number of people. I am an ex player but a keen spectator on TV.
My understanding is the players are to be listed firstly by their score, then by the number of holes played
and if scores are level (on same number of holes) then alphabetically.
i have always thought that is part of golf etiquette.
It is certainly the case on British TV coverage including the European Tour, Australian TV coverage also abides by that.
Not sure why American TV coverage should be different to all the rest.