Just because the government has done bad things is not evidence that they were involved in a conspiracy to kill JFK. After six decades there is no credible evidence of such. Steve's point is a good one. Many other government conspiracies were quickly exposed including arguably very simple ones like the Watergate break in and cover up. If the sitting president couldn't cover up Watergate involving a handful of numbskulls, then there is no possibility that an ongoing cover up of complex conspiracy to assassinate JFK continues. And why would current governmental officials perpetuate any such cover up? It's laughable. The cover up claim is just an excuse for those who have been unable to provide credible evidence of the involvement of anyone other than LHO in this crime. They need a cover up to explain why there is no evidence.
If you visit the conspiracy sites you'll quickly see they are filled with posts about such ugly/nasty thing, real or imagined, the government did. Mongoose, Northwoods, MK-Ultra, this or that bad guy that was connected to the CIA or government. It's endless. They seem to think that if they can prove how horrible things were, how such evil people were around, that that is evidence they murdered JFK. And JFK was going to end all of that nastiness but was stopped before he could. They did bad thing "A" and "B" so they did bad thing "C", murdering JFK.
As I said above, I can prove that Castro and his government did bad things too. Execute political dissenters, torture and arrest opponents, support bloody dictators like Mengistu. Is that evidence that he was behind the assassination? Of course not. The conspiracists who say the CIA did it would dismiss it out of hand. Rightly so.
As to coverup claims: It simply can't be done. And pointing to other conspiracies - which were exposed - is contradicting the conspiracy claim that this conspiracy - far more complex and extensive - was somehow the one that was kept secret.