The Katzenbach Memo on Monday morning after the assassination made sure that Oswald was regarded as a lone nut and the only suspect.
Thus, any more investigation was unnecessary and cut by the roots.
Life in Irving before the assassination:
Before the assassination Oswald would be an ex marine, former member of the civil air patrol, and befriended with the rightwing De Mohrenschildt, a Dallas Petroleum Club member.
However, at the same time he would be a Fair Play for Cuba activist associating with Pro Castro Cubans and publicly advocate for a "Hands of Cuba policy".
Ruth Paine apparently had monitored help organisations in Nicaragua helping the Sandinistas who in 1961 formed the FLNS in their fight against dictatorship.
Michael Paine had a file cabinet with information about Pro Castro Cubans ...
(Wait a minute, could Oswald be furnishing Michael Paine with such information?)
Oswald, being a nobody, would get huge media attention for handing out only a few leaflets. Heavy TV cameras would show him handing out those leaflets and interview him later in the studios where he eloquently would answer questions about international politics.
(Now would you consider the following to be a matter of coincidence?)
Hoover made a memo about Oswald's name being used in intelligence operations while Oswald was still in Japan. The CIA had a 201 file on him.
The Sandinistas claimed to be Marxist Leninist and were supported by the USSR. Nicaragua was subject to counter espionage from both the US and the USSR.
Castro claimed to be a Marxist Leninist. And guess what, Oswald claimed to be a Marxist Leninist.(to get more credibility as a "Pro Cuban"?)
(Rather than being a coincidence you may wonder if Oswald formed part of a small scale counter intelligence operation, a kind of a 9 to 5 spy job)
If so, it could certainly be necessary to cover this up. Imagine that Oswald had become a triple agent for the USSR/Cuba. A WWIII could wait around the corner.
(Disclaimer: Citing from memory only, elaborating on a working theory)