> I find that the use of "logical fallacies" to be an intellectual smell as well.
I find there's an over-obsession with logic in some discussions too; as in, ancient-greek-style modus ponens stuff. To me, that's not particularly interesting when it comes to the real world[1]; after all, logically-speaking we could just be a brain in a jar, or whatever.
An argument being "logical" (as in, not self-contradicting) is not enough to make it credible; it's just a very low bar, which lets us dismiss the most nonsensical claims quickly. Arguments which cross the "logical" bar should also align with empirical evidence, have a likelihood that's at least comparable to alternative explanations, etc.
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I don't think "conspiracy theory" has quite become a thought-terminating cliche yet. It can usefully describe a common failure-mode in thinking.
In particular, conspiracy theories become less and less likely as they're inspected closer and closer; e.g. requiring even more people to be "in on it" (making it less likely to be kept secret), requiring ever-more elaborate epicycles to explain-away observations/experiments/events, etc. They can't be disproved, but who cares? That's not a good enough reason, on its own, to affect anything.
Another legitimate use of the phrase "conspiracy theory" is a particular case of "affirming the consequent" (i.e. getting implications the wrong way around). For example "if X is true, Y would make so much sense", where X is the "conspiracy" and Y is some well-known/self-evident fact about the world. This might be true, but the mistake is to treat Y as proof of X: this would give us "if X is true, Y would make so much sense, so X is true", which is an elaborate way of saying 'if X is true, X is true'. Here Y isn't actually proof of anything, it's just a distraction.[2]
[1] In artificial contexts, like mathematics and programming, I find logic to be fascinating and rich; e.g. I spent a lot of time studying topics like type theory and co-induction at grad school!
[2] The "logical fallacy" here is assuming (X -> Y) -> (Y -> X)
PS: From a bayesian perspective, 'if X were true, Y would make so much sense' is evidence for X. It's not proof, but it makes X more likely (essentially by ruling-out the potential for Y to disprove X). However, (a) the change in likelihood depends on the prior probability, if X were wildly unlikely then such weak, indirect evidence cannot make up for that; and (b) this sort of nuance of probabilities is negligible compared to the wild chains of "logic" spewed by the conspiracy theorists I know.