The answer is an emphatic NO as far as JFK's assassination is concerned! There was so obviously a cover-up after the assassination that the logical inference is there was a conspiracy. The conjecture since then has been about who the conspirators were. The problem is the conflation of those theories with other ridiculous claims such as a flat earth or bogus moon landings where the evidence speaks for itself.
I've heard many people, not necessarily the theorist types who actively promote the idea but ordinary Americans, say they simply can't believe that a nobody like Oswald could change history so much, could kill the most powerful man in the world. There just has to be something more. It's an emotional, psychological need to believe in something larger, that great events have to have a great cause or force behind it and Oswald simply can't be that force.
So, yeah, I think there is/was an emotional or psychological desire or need behind the belief in a conspiracy. I think some of that is behind the conspiracist theorists too but they are motivated by more than this emotion. It may have started with that but it's more. There's probably also a psychological need for lone assassin believers to think that "the government" didn't kill JFK either, that there wasn't a CIA/FBI conspiracy. That is that one's own government couldn't do such an act. Mom and apple pie and all that.
As to the coverup: If you know there was a coverup then you must know who they covered up for, right? There must have been a reason for this coverup other than because of incompetence or they didn't want to reveal classified information, e.g., the CIA and the wiretaps, et cetera, or they didn't want the covert war on Cuba revealed. That's a innocuous type of coverup, one that did take place, but not a sinister one. I assume you mean covered up for the murderers, the real perpetrators of the crime? Covering up for incompetence or for national security reasons is different than covering up for those who did the act itself.
But you admit that it's just conjecture as to who were the conspirators? The same ones that the cover up was for?
So how many coverups over how many years have we had? The Warren Commission was ordered to cover up (again for who?) and then all of the people remained silent? There are some staffers who worked for the Commission who are still alive. Why are they remaining silent?
What about the HSCA? Coverup? The Rockefeller Commission? Coverup? The Church Committee? Coverup? How about all of the news organizations and reporters who investigated this? Did they cover it up? Seymore Hersh says he looked into it and found nothing. Tim Weiner, ABC News, the NY Times. It's a lot of people covering this up for a lot of years. People who had no reason, no benefit, to do so. In fact, they had much to gain by revealing it. So, again, who were they protecting?