There really are bad men plotting awful things and our history is full of their activities.
No matter how true that is, it doesn't mean that all of the plots and awful things one suspects have happened the way you imagine they've happened, and certainly not with all of the details concocted in many conspiracy theories.
There's also the matter of just how much power these "bad men" have. Some conspiracy theories require nearly magical levels competence, secrecy, coordination, cooperation among apparent rivals, etc.
We really do live in an absurdly corrupt kleptocracy where a nebulous shadow government...
Absurdly corrupt compared to what? There has been, and probably always will be, abuse of power and influence. This has long been possible with diverse, uncoordinated, and shifting centers of power, and often with blatant indifference to secrecy (as monarchs and dictators can often do what they like without being questioned).
Your proof of this "nebulous shadow government" is what? The lack of proof is proof of how well they hide themselves? You think people who don't believe it's there have the burden of proof that it doesn't exist?
Suppose tomorrow some prominent politician is killed. Could a crazed lunatic do such a thing on his own? Yes. Could a conspiracy, large or small, do such a thing? Yes. Does evidence matter, or is it a conspiracy until proved otherwise?
I have no problem believing conspiracies are possible, but I do need proof of a specific conspiracy before I yell conspiracy, and I need something a lot more plausible than secret giant space lasers and buildings rigged for controlled detonation right under the noses of their occupants (all for no good reason, when having a plane smash into a famous building, killing thousands, regardless of whether the building collapses or not, is more than enough excuse to rev people up for a war).
There are some people, however, who will never, EVER believe that an important politician was killed by one person acting on their own (I'm not trying to invoke JFK specifically here, by the way). No matter how good the apparent evidence, it must have been faked. No matter what eyewitnesses say, it must be that they are in on it, or have been coerced into telling the dread "official story". Every inconsistency in eyewitness testimony, regardless of the fact the witnesses are well know not to be terribly reliable, becomes proof that something different than the "official story" must have happened.