“Back to the hat, Rav Soloveitchik ZT”L from YU as well as the current Rosh Yeshiva, Rav Schachter, both wore hats as well.”
Many of the other great Roshei Yeshivot at YU wear black hats in including Rabbis Willig and Tendler.
Rov Soloveitchik z’tz’l didn’t always wear a black hat; there are many photographs of him in a straw hat. He would be the first to agree that ones’ insides were more important than ones’ outsides, and many of his students didn’t wear a hat at all.