Actually, the most powerful group in the House are moderate Republicans because they are ones who provide the critical margin one way or the other. They are the reason a GOP shutdown cannot/will not happen.
The House conservatives made a fundamental strategic error in assuming, as people like Rosendale did, that a small GOP majority empowered House conservatives. But that was only true for purely internal matters. Outside the caucus, in the House as a whole where legislation actually passes, the tiny margin empowered the most moderate members of the GOP because they always had the option to get at least some of what they wanted by making deals with Democrats..
That reality handcuffed McCarthy, is now handcuffing Johnson, and would handcuff any other Republican chosen as Speaker.