“Rav Moshe’s great-grandfather Rav Dovid, was a Koidenover Chosid, as was Rav Moshe’s father, Rav Dovid, in his youth.”
“The Steipler’s father (Rav Chaim’s grandfather) was a Chernobyl chossid.”
The OP intimates that they were great because they came from Chassidish stock. Maybe their greatness came because they stopped being Chassidish.