There’s no doubt that the fewer movements a pitcher makes, the fewer mistakes he can make. That’s why it works so well for new pitchers. But once a pitcher has been pitching for some time and has developed his own “style”, it becomes much more problematic and more of a tossup whether they’ll be able to perform well from the stretch.
I’ve always kept track of how pitchers do with runners on or not on(stretch or not), and I can say with a fair degree of certainty, that pitchers in general perform better from the windup. How much of that is because they’re distracted with runners on and how much is because they just don’t pitch as well from the stretch, I wouldn’t want to guess. But there certainly is a noticeable difference in most pitchers. 