Sure it is. The problem with the hypothesis is that the President of the United States could not go violently insane, or be believed by large numbers of high-ranking government officials, to be going violently insane (whether true or not) without that belief leaking out to many thousands of people, if not millions. This is especially true in JFK's case, where practically every second of his presidency, and of his last few months in particular, has been pored over by untold numbers of researchers looking for a more satisfying explanation to his assassination than "That kook Oswald did it."
Even if "They" managed to keep such beliefs about violent insanity swept under the rug in the early '60s (extremely improbable, IMHO, but potentially not utterly impossible like it would be today), there's no way it would have stayed hidden after November 1963.
The Kennedy family refused to acknowledge more than one of JFKs medical conditions, admitting to Addison’s disease only recently.
As far as actually asking him to resign is not an essential element of determining whether or not he should be removed from office. Because of the Cuban Missile Crisis, the awareness that JFK had his “finger on the button”, plus the drugs he was taking, might have been enough.
Again, it was common knowledge at the time, though wrong, that cortisone in large doses would make you insane. Had whoever asked a physician familiar with cortisone at the time, they would have told you that.
Then again, I mention the movie released in 1956, at or near the height of James Mason’s popularity as a film star. The very idea that the President might act like that could be all that was needed.
Would they wait until the President was acting like a lunatic? I doubt it.
And I have no doubt that even today the Kennedy family holds onto a large amount of embarrassing information about JFK that has never seen the light of day.
But the bottom line is not to disparage JFK, it is to point out that there is, that there must be, some consideration given to what to do if the President of the United States no longer has the judgment needed to authorize the use of our nuclear weapons.
The office is more important than the man.