TL;DR: I think it's a play to help Trump (if that's even possible) at taxpayer expense.

Another way to look at it, is that she and the Freedom Caucus are trying to make it impossible to fill the speaker position. Last time took 15 tries over 4 days. We have a pro-tempore speaker, but legislation will take a back seat to filling the Gavelmeister (I mean speaker).

This data is from Sept. 20 https://www.cnn.com/2023/09/20/politics/mccarthy-house-speaker-vote-margin-numbers-dg/index.html

• 31 far-right Republicans who have repeatedly voted against McCarthy

• 18 moderate Republicans in districts Biden won in 2020

• 172 other Republicans

• 212 Democrats

• 2 vacancies

That's 435 seats (2 vacant). From 2001 to 2021, the Senate spent an average of 164 days in session each year, and the House spent an average of 149 days in session (source https://ballotpedia.org/117th_Congress_legislative_calendar). The annual salary of a rank-and-file Member of Congress is $174,000 (source: https://www.congressionalinstitute.org/2019/02/21/how-much-do-members-of-congress-get-paid-2/)

So each day of this clusterbuck, each member of congress is getting just over $1,167. Multiply that by 433 (the number of filled seats in Congress) and we spend $505,651 or half-a-million dollars each day for congress to twiddle their thumbs. It cost the US taxpayer more than 2 million dollars to elect McCarthy, and now we're going to pay to find a replacement.

While the republicans have the majority, it is fractured by extremists and moderates. The democrats won't vote for an extremist republican, so most likely 212 (Dem) + 18 moderates = 230 Nay, even if 172 others + 31 extremists say yea, the vote fails. But if the 31 extremists say nay to a moderate, it's going to take democrats reaching across the aisle, and then Gaetz plays the ouster card again.

We have a continuation resolution to keep the Government going for 45 days, or until Nov. 14. If The Freedom Caucus keeps the speaker position churning, the government may shut down because they are too busy playing "who gets the gavel?". The far right is pushing to cut funding for the F.B.I. and the Justice Department (source https://www.nytimes.com/2023/08/04/us/politics/trump-house-budget-fbi-republicans.html) because this could help save Trump. But even if they got what they wanted now, I don't see New York stopping their trial, and I don't see Georgia just rolling over. Trump's bacon is being held to the fire. All the Freedom Caucus is doing is creating Chaos. I could hope their supporters would see this as an expensive Hail Mary, but I doubt it; they will probably get re-elected and this circus will continue.