The actor who plays Newman on Seinfeld was also in JFK, and revives his JFK role for the show:

Of course it was Kramer who shot JFK, Martin Luther King, and Malcolm X.

The films premise rests on the assumption that Kennedy was some sort of liberal ushering in a new era, the Camelot myth. And that's all it is, a myth. Its origins are with the intellectuals that the administration wooed during its term and administration officials seeking to distance themselves from Vietnam in the wake of the Tet Offensive.
The facts are quite different.
During his time in congress and the senate Kennedy was on good terms with McCarthy and the other ultra-right joining in the red-baiting of Adlai Stevenson and other New Deal leftovers, he maintained a hawkish stance on the cold war through his time there.
His presidential campaign again took a hawkish stance insisting Eisenhower had allowed a "Missile Gap" to develop - of crucial importance is that he won the election by a mere 100,000 votes, could Joseph P. Kennedy with his shady business connections have had a hand in this?
On civil rights he dragged his feet, doing little except when dead organisers would appear on the evening television news in the cultured north east and overseas - while at the same time COINTELPRO continued to harass them and stir up the KKK.
Abroad it was Business as Usual. Designating efforts at removing a ruling elite or social reform or neutrality as "radical nationalism" or "communist infiltration" and dealing with them accordingly: arming and training and directing the efforts of the dictatorship in power or finding elements of the military willing to overthrow the existing government, of particular notoriety would be Operation 40 (the failed Bay of Pigs invasion of Cuba)/Operation Mongoose (terrorist war against Cuba) and the outright invasion of Vietnam when their proxy regime could no longer manage the situation.
There are multiple sources too numerous to mention, but since I'm reading it at the moment I'll recommend Killing Hope by William Blum.

Here is my theory: perhaps Kennedys continued problems with the back wound he received during WWII when PT-109 was sunk, possibly aggravated during one of his frequent extra-marital liaisons, resulted in him wearing a brace - which restricted his movements. Because of it on that fateful day in Dallas he was unable to duck down after the first shot.
Its not without support, some have suggested the wild actions during the Cuban Missile Crisis were the result of the painkillers he was taking due to his back problems.

There is another problem with the premise – at its core it rejects an instiutional analysis and instead offers the notion that all the problems resulted from a bunch of thugs seizing power and running it for their own benefit, but before that everything was a-okay and everything can be again.