Here's just a handful of instances where conspiracies turned out to be true.
https://www.corbettreport.com/5-conspiracy-theories-that-became-conspiracy-facts/
There are many more.
Also, do you consider plotting/enacting a coup as a conspiracy to commit murder?
By definition, that's what a conspiracy is - people conspiring together to perform and illegal, subversive or wrongful act.
If so, then there are a plethora of examples that I'm sure you're aware of from Chile to Iran and hundreds of more coups and coup attempts throughout the world. Many coups have substantial documentation as evidence that only emerge decades later as they are hidden from the public.
There is a big difference between small scale conspiracies that happen on a daily basis and outlandish claims that would require tens of thousands of people to stay quiet as the case with "inside job", "moon landing", "flat earth", etc.
Magnitude is important when discussing this.
Because there are a handful of instances where conspiracies happened does not add anything to the validity of the conspiracy claims i mentioned.
People commit conspiracies all the time.
But why would you think what CIA did in Chile works in conspiracy theorist favor?
That doesnt add validity to the outlandish conspiracy claims people make. It actually takes validity away from them. It shows how extremely hard it is to keep this stuff a secret even by a secret agency.
And wer talking about stuff all major world powers do all the time. Covert warfare, spy stuff, all publicly well known and documented.
The problem with conspiracy theories, which is why i find them in complete contrast to scientific thinking, is that they assert a conclusion they want before hand and then go into cherry picking information that suits the narrative.
Instead what should be done is collecting of all the facts you can find and then let the facts lead you to a conclusion, whatever it might be.