This was not the old normal. Nixon would not have done this. Also, there's no evidence Nixon believed this. There's a lot of thought in conspiracy circles around Nixon's mentioning the "Bay of Pigs" issue in recordings. Nixon was not trying to uncover a deep state involvement in a massive conspiracy to kill Kennedy. Nixon was trying to uncover evidence JFK screwed up the Bay of Pigs invasion and overall was a screw up in order to undermine Kennedy's legacy for political purposes.
The conspiracy thinking acts of a number of psychological levels. My response won't cover all of them. On one hand, it's a vestigial hold over from the era of Big Good Government. It's the idea that the government is effective and can do anything but taken to a dark, malicious direction. That lingers into today so even people that think government is too incompetent to handle the basic affairs of society and state also think there's a dire cabal of actors and agencies with total power and influence. Essentially, they are too incompetent to fix a pothole but can mind control you and not get caught.
On the other hand, born out of a sense of Big Government to some degree also born out of human needs, it's a matter of placing the world in order and patterns, making it able to be known and therefore making it manageable and to some degree safe. If Kennedy isn't killed by an orchestrated plot that was planned and outlined and where the outcomes were planned and orchestrated, what that means is that the world is impermanence. That means that you and I and the sense of "us" is subject to forces of happenstance, uncertainty and randomness. It means that the tapestry of relationships and consequences is vastly more complex than we can conceive and predict. It means that tapestry is not active, planned and controlled but passive, unplanned and uncontrollable beyond a limited level that can only manage what is within it's power to. It means that chaos only takes one major disruption and can happen at any times. It means we are not masters of fate. We are subject to it. When that is good, it is a happy accident. When it is bad, we are victims. We are the observers, the listeners and the reactors.
There is no man behind the curtain. That's just a breeze blowing because someone forgot to close the window. What happened on November 22, 1963? A man was killed because power and position don't matter to mortality. He was killed by a mentally ill man in his early 20s who grew up in an abusive upbringing and developed a narcissistic need to feel important and provocative to get attention. This was a man who was never loved and wanted to be famous or at least infamous. He developed a righteousness for himself in the form of ideology, which he adopted to feel important. He regarded being provocative as just someone else's problem. And he took his training as a sniper and all his psychology, got in a window at a place he worked because he was going to kill someone (he tried and failed before and he had other targets in mind before Kennedy) and this would be the time and place. And he killed a famous person to be important.
There were many more people like Oswald out there at the time. There still are those types of people today. Some have the chance to do evil. Some do not. It's happenstance in either case. The world is good and bad and we are observers, actors and reactors in it.