The more likely reason is that the Soviet Union had it done.
It’s certainly what Ion Mihai Pacepa thinks, anyways, as does Markus Wolfe (well, technically, the latter indicated it was the Cubans, but it’s pretty much the same deal). And considering Pacepa worked at the DIE and had more than a little involvement in some KGB disinformation operations (heck, he practically wrote a book about it), I’d be more inclined to believe the USSR was the party responsible for JFK’s assassination.
Besides, I doubt that GHWB, whether he is contemptible or not, would have had much influence during that time anyway. He didn’t become CIA director until 1976, and besides which, he was barely even entering politics anyways during that time, being state-level at best. And as far as LBJ, he’s a crook, a very contemptible one at that, and he’s definitely one of our worst presidents (probably the only ones worse than him are Obama, Clinton, and Carter), but I don’t buy him being involved in the JFK assassination. For starters, if he wanted to depose him, he wouldn’t even need to commit murder against JFK. All he needs to do is leak a story to the press about how JFK slept with an East German agent, even blackmail a few reporters, and then he’s got easy access to the presidency. Plus, the assassination was BEFORE the amendment calling for a formal line of succession for the Presidency was ever ratified. There’s also one other factor one needs to take into account: He apparently didn’t even know about LHO’s involvement in the assassination until three days afterward via the CIA debriefing him on that bit based on that memo that was released. How could he have hired him to do so if he didn’t even know him beforehand? Heck, try as I might, I can’t even imagine the Mafia doing something like that to JFK, even WITH their grudge against him. I’m pretty sure the mafia had a grudge against FDR for shutting down some of their operations as well, yet they didn’t try to kill him even when they had the opportunity. And somehow, I don’t think they’re the types to use Radu to poison hitmen to silence them, that being more of a KGB method of assassination. And don’t get me started on the CIA, either. Even assuming they were capable of killing a President they didn’t like (and believe me, there have been plenty of presidents besides JFK that they also disliked, yet they didn’t try to assassinate them at all), there’s the fact that they really don’t have much to gain from the assassination anyway.
As far as why they’d be classified or covered up, gee, maybe it has to do with the fact that we just barely managed to avert nuclear war a couple years beforehand with the Cuban Missile Crisis? Heck, LBJ actually rejected reasonable attempts at dealing with North Vietnam given by his advisors and implied that their plan would result in World War III. And don’t think that just because the USSR collapsed that means we don’t have to worry about national security. The USSR might be gone, but Putin seems to be dead-set on restoring that depraved system, so it would be a very bad idea to release the documents. Until Communism is completely gone from Russia, to the extent that Communism itself is banned as a political party, it’s still a threat.