The Cabin in the Woods (2012)
1 stupidity
Directed by: Drew Goddard
Starring: Chris Hemsworth, Anna Hutchison, Kristen Connolly, Fran Kranz
Plot hole: When Dana realizes that the puppeteers made them choose their own deaths (while standing in front of Fornicus in the elevator) she does so by watching the puzzle ball he holds. But she never saw the puzzle ball back in the cellar. Only Curt handled it briefly and is shown approaching her without it when she starts reading the diary.
The Director: This is all most unpleasant. I know you can hear me. I hope you'll listen. You won't get out of this complex alive. What I want you to try to understand is that you mustn't. Your deaths will avert countless others. You've seen horrible things: an army of nightmare creatures. And they are real. But they are nothing compared to what lies beneath us. There is a greater good, and for that you must be sacrificed. Forgive us... And let us end it quickly.
Trivia: One of the creatures glimpsed jumping out of the lift is one of the small monsters which attack people in the subway in "Cloverfield". The director of this movie, Drew Goddard, wrote Cloverfield.
Question: Is there a reason, that a facility full of monsters would ever, under any circumstances have a System Purge button? Is it just to make satire of the fact that the antagonist is usually stupid?
Answer: As you said, it is a satire of the common Deus Ex Machina trope you find in such films.