Remember also that Gaetz had a plan B in the event that Dems voted to keep McCarthy in power: "you see! our house majority leader is supported by the enemy! RINO!"
It was win/win for Gaetz. It's always going to be win/win when the goal is to prevent the Federal Government from functioning. These Freedom Caucus district voters want their reps to just gum up the works. A weak, dysfunctional Federal Government is the goal for these sociopaths.
And I mean sociopath in the truest sense of the word: they do not want to participate in or be governed by a society that they disagree with. The problem with the United States, as they see it, is the "Union of States." They've given up on the Constitution entirely.