They have done it before to the Paleocons and Libertarians.
[Citation needed].
When has the Social Conservative wing of the Republican party
ever been dominate in the coalition? What years exactly?
The likes of Turtleneck and Bill Kristol are still running the "republican" party, and Liz Chaney is still around.
American Political Parties aren't like European ones. There is no single organization that maintains some role of who's a Republican and who is not. In many respects American political parties are like America itself, there's a bunch of small, local Republican Parties that all band together, and even at a local level, they often do not control who identifies with the party and who doesn't.
But let's go down your list here. By Turtleneck I'm assuming you mean the Senate Minority Leader Mitch McConnel. I would point out that Senator McConnel has given the Dems some of the biggest and greatest losses of the last decade, with much of the present line holding against the worst of Biden's overreaches coming from him basically creating a judicial superhighway as well as sticking to his guns on the appointment of Kauvenaugh where prior Majority Leaders in the Senate likely would have balked and pressured the President to withdraw the nomination.
Bill Kristol has absolutely no position in the Republican party and is just a commentator in a magazine that is primarily read by left wingers anymore. He's not an elected official and he's literally running on fumes of past influence.
Finally, Liz Cheney... I'm not sure what you want? Her local Republican party has basically kicked her out, the Republicans in the House have marginalized her as much as they can as the minority party, and she's being primaried so that she won't stand as the Republican candidate for her present seat in the US House. There's literally nothing more that can be done to her to get her out of power. In the US Representatives a PERSONALLY elected to hold the seat they do, and barring a recall election (which is very rare for House members since they have such short terms to begin with) or actual criminal activity which forces their removal by the House itself, they're literally nothing more that Republicans could do to get rid of her. All her present influence comes from the fact the Majority Democrats in the House have propped her up along with the mainstream media, neither of which are under the control of any aspect of the right.
You seriously need to stop commenting about the status and history of the American Right. you have no clue as to the actual power dynamics and history of the movement, just some weird abstract view of it that appears to be based on left wing propaganda.
