One of the worst things JFK did was kill off the men’s hat as a fashion accessory.
That's a myth. Rather than being the first president to go hatless at his inauguration, he was the last to wear a traditional silk top hat. He took his hat off when he was seated on the inaugural stand, and left it on his seat when he was sworn in and delivered his address - it is visible there in some photographs. Apart from that, he wore the topper for most of the day's events.
JFK preferred to go bareheaded, but that trend had already started years earlier.