Even NWA territories had big guys often in major positions. With freakishly big guys who couldn't really work they would often build them up so they could challenge the champ and "steal a house" by getting a main event title match out of them before they got exposed.

And their top stars like Flair, Sting, etc weren't "big men" but weren't small. I don't think Dusty Rhodes was doing a lot of high flying moves.