The problem with conspiracies is not that there always exists a paper trail, but that there quite often doesn't. Iran-Contra or Watergate may have been revealed, but the notion that all such illegal or immoral actions by the government have been made known to us is laughable. I mean, the statement that we know the "origin and full truth" of everything that every person who has ever been in power ever did (and used that same power to cover up) - that's the most ridiculous assertion I've ever heard.
Of course some conspiracies have succeeded. We know who killed Caesar, for instance. And of course there are some we don't know about. Some secrets are successfully kept; that's obvious. Also, not all conspiracy theories are bunk. If some guy asserts at any point in history, "So-and-so is involved in a conspiracy to kill X and Y", or "President So-and-so is involved in a conspiracy to profit from his position", and his assertion is true, then that's a conspiracy theory that wasn't bunk.
What you're asserting is more ridiculous than holocaust denial. The holocaust obviously happened, but it takes empirical evidence to know that. Saying "powerful people throughout the ages have been involved in schemes, and the public doesn't always find out the details" - that's something you don't even have to think about.
There is always, always, always a trail of evidence, and you can always follow it back and uncover the truth from it. That is because humans have never ever been able to cover up everything and every detail, and it only takes some evidence to lead to another bit of evidence to another bit of evidence to another bit of evidence, eventually cracking open what happened. The bigger that which is attempted to be hidden, the more residue is left behind which will uncover the truth. Not to mention the factor that humans are severely incompetent, which is the reason evidence exists and not all loose ends are tied (which all loose ends can never be tied anyway) and why Illuminati-sized nefarious conspiracies are impossible, because some things will go wrong and people will screw up.
If I steal cookies with friends when I'm 7, then no, that conspiracy will have a likelihood never to make it out. If I knock over a bank with a gang, that's a different story. If I kill the president or fake a space effort, that's a very different story. If I oversee and take part in the genocide of millions of Jews, homosexuals, leftists, and disabled persons, that is a very different story.
A real conspiracy and how a real conspiracy unfolds was shown with Watergate. People cannot keep a lid on anything, evidence is always left behind, and people cannot shut up. And any action you try to take to cover up a loose end and/or to hide the truth and try to keep a lid on it makes more loose ends and more evidence. And the bigger the effort, the more chance for screw ups and people talking and evidence and loose ends, and any major conspiracy requires it to be big since it requires a large infrastructure and it requires power, and power is based on size and invites growth in size.