Why was there such panic in the establishment? Why does the Warren Commission have every appearance of a coverup or a whitewash?
Were there powerful interests that were afraid unrelated secrets would be revealed if someone probed too deeply? (I'm thinking, for example, of the events immediately after 911, when the Bush administration hustled the Saudis out of the country.)
Was there a fear that Americans would lose their naive faith in democracy if they started to suspect that this country was not much different from less "civilized" parts of the world, where assassinations and military coups were a standard method of transferring power? In particular, would the changes in policy between the Kennedy and Johnson administrations have seemed more suspicious if there had been questions about whether it was all planned?
As we constantly see in the case the of Tea Party types, people who are up to no good tend to panic if someone else does what they're already thinking. This is why the right freaks out every time someone points to the proliferation of hate groups or notes that the latest mass shooter was a fan of Alex Jones. So even if Kennedy's killer was a lone gunman, everybody who'd been fantasizing about seeing him dead might have reacted similarly and started doing whatever it took to make sure their actual plots could never be pinned on them.
There are a lot of festering questions about the Deep State activities of the early 60s, and saying "Oswald did it" doesn't make them go away.