Didn't hurt Landry to have guys like Dorsett, Walker, Preston, and Reeves and Hill before that either. Plus remember that our OL in those days were definitely not the size these guys today are.
I think another reason is that is was a staple of the Cowboys for so long that once the team was successful at it there was a trickle effect to the newcomers and eventual replacement starters. They learned from successful players who could pull off the screen play. And the Landry regime was a very long and very successful one.
It may just be harder for an entire team to learn how to run that play especially with those huge offensive lineman. Just a guess.