BINGO! In 1960 my Dad, uncles, and friends fathers had hats. In 1961 only one bald uncle still wore one. Mom said it was a fad (going hatless), but that was the end. Hat's made you look old and since JFK, every middle aged man wanted to look young.
JFK would have wore a hat as well if he was bald but he still had the hairline of a 10 year old into his 40s. For some reason certain Irish men never lose a follicle of hair nor even go gray. Reagan was another example.
Jack Kennedy certainly helped advance the trend, but I think it was a part of a broader cultural phenomenon informed by intellectual alienation and radical egalitarianism beginning in the early '60s, in which "youth" was revered over old age (and wisdom).
It was greatly hastened by the folk music movement, the Beatles' arrival in America and by the rapid rise of the same dope-smoking lefty Peace Creeps who now (having become old people themselves, but absent any acquired wisdom) run the government and the schools, and also dominate the entertainment industry.
Exactly. JFK represented the new cool back then.