I highly doubt that a secret in the caliber of “let’s
kill the President” can be kept by so many people for
such a long time.
Agree.
However, what if that wasn't the conspiracy?
What if the conspiracy was, "let's avoid war with the USSR"?
If the US Government knew of or suspected USSR involvement in JFK's assassination: their choices were essentially "war with the USSR", "look like fools who bowed down to the USSR", or "pretend that Oswald was a lone, crazy guy."
In other words: not a conspiracy per se where the government was en masse covering up some specific thing they knew to be true. I agree with you that feels implausible. Especially since presumably a significant portion of the government would have been opposed to the assassination or the cover-up.
But it might have been more of a concerted effort to look the other way. Like, "If we investigate Oswald and the investigation too closely, the trail might lead to Russia or one of its satellite states, and therefore war, and therefore nuclear war. So therefore let's all agree that Oswald was a lone gunman because it sure beats war with the USSR."
That does not seem impractical to me.
Remember, the country was still reeling from the Cuban Missile Crisis, and the chilling possibility of having narrowly avoided nuclear war.