It's much more likely your pitchers are flat out tired and sore than they re afraid by the time October rolls around. Severino has ace stuff. He isn't afraid of the competition. And he doesn't need a $30mill binky to draw away he glare. If that was the case, he would have topped out in the minors. The list of AAAA players with 97mph fastballs has a higher number on it than either you or I could give a name to.
The Yankees don't need Cole, which is a good thing because he will be an Angel or a Dodger. But the Yankees do need actual rotation depth and to stop pretending Jordan Montgomery is the solution here. If the Yankees go sign, say, Tanner Roark and stick JMont in Scanton where he belongs, they will still be favorites in the AL East. And if they manage Severino, Tanaka, and especially Paxton's innings to a respectable 150-180 during the regular season, I think you will see a lot of this "fear of the bright lights" is magically gone come October....