It’s probably been a while since your read the book, so you have forgotten some things.
For one thing, the guild navigators are prescient and guide their ships across interstellar (and even intergalactic) distances faster than the speed of light. They use their prescience to pick routes where the ship arrives safely instead of plowing through a stray planet. They also use it in a less obvious fashion to maintain the political status quo. They try to avert political crises because they like their position in society and don’t want anyone changing things (which explains the long stasis of the Empire). People did at one point use computers for safe navigation, but they were slower and they weren’t prescient. The possibility that prescient machines might one day be built is the entire reason why Leto II spends so much time breeding humans in “God Emperor of Dune”. He’s looking for anything that can be an edge against the machines, and he hits the jackpot when he discovers that one of his descendants is not prescient, but is invisible to prescients. She and her actions cannot be seen in future he predicts. She and her descendants can safeguard humanity against any form of hostile prescience, machine or alien or otherwise.
Synthesis of spice was a long–term plot element in the series. The Tleilaxu eventually master it. Keep in mind that it isn’t a small–molecule drug either; it’s an alien life form.
Mentats were intended to be a replacement for computers and databases. They were frequently administrators and advisors, and often used their capabilities to convince people. But that wasn’t the goal of their training.
The Bene Gesserit have eidetic access to every memory of every one of their female ancestors. That is actually very impressive; most people don’t even have eidetic access to their _own_ memories, let alone the ability to easily recall secret information known only to their ancestors (such as the password to a safe). The Reverend Mothers can transfer all of their ancestral memories to another, so that the new Reverend Mother has access to the memories of both sets of ancestors. Long chains of Reverend Mothers gifting their memories to each successive Reverend Mother results in the Bene Gesserit having access to the ancestral memories of virtually every race or group of people that ever existed (except the Jewish, who successfully hid themselves even from the Bene Gesserit but otherwise still exist, which is a plot point in one of the later novels).
They can also command people to act. By a trained effort of will they can tell you to get up and dance a jig, or to slit your own throat, and you’d do it. That’s an ability worth respecting, which explains why the Baron Harkonnen took care to put a deaf guard in charge of a Bene Gesserit prisoner.
> So the Butlerian Jihad exists only in a plot-armored world specifically designed to make it work.
Ultimately, however, none of that matters because this statement is what you’re really intending to argue. It’s overly reductive, and it can apply to any work of fiction. Authors naturally build or select a setting where their story makes sense. Frank Herbert (and a few others like Tolkien), went further than that and invented world–building. This excited a lot of people and sold a lot of books, and now you’re cynically dismissing it by calling it “plot armor”.
Ultimately Herbert’s point was that people should strive to be humans, not animals or machines or slaves to people with superpowers. You can’t dismiss this philosophical stance merely because he used a fictional world to illustrate it. It can be true in the real world just as it is in his books, so to refute it you will have to be more clever than that. More human, perhaps he would say.