From the day Oswald arrived in Dallas on a bus from Mexico City - October 3 - to the day of the assassination almost two months later (50 days to be exact) no one in the government knew where he lived during the week. They had no idea what he did or went during those weekdays and nights. And it was only on October 29 that Hosty said he learned that he was living with the Paines on weekends. And the first time he ever talked to Oswald was in the police station after his arrest.
So for almost two months he was off their radar. Incompetence, bureaucracy, sloppy work: real human beings and not these sinister all-powerful groups that conspiracists see everywhere. Even today.
As to the alleged decades old coverups (plural): let's put it this way. The idea that Republicans and Democrats, who hate each other like two religious sects, could or would agree to cover this up all of these years, and remain silent about it, is utterly and completely bonkers. It cannot be done. Human nature and politics and the way people behave forbids it. I can see how some conspiracy believers in the UK or abroad could see this happening. They don't know what we know, how the government on all levels operate. But no American who knows how the two parties loathe one another, who know about the bureaucracy we have, the personality conflicts, the turf fights, the incompetence of how government works (as I noted above on their non-monitoring of Oswald) should believe this.
But somehow they do.