You are entitled to your opinion about what is acceptable. I disagree. We need an aggressive, conservative in the leadership position. The Speaker is the critical position. We don't need Boehner's hand picked deputy as his successor. Nothing will mitigate McCarthy's selection to the position.
And the new Leadership HAS to represent the WHOLE caucus. Not just us or them.
The caucus has to represent the GOP voters. 62% of GOP voters believe that they have been betrayed by their party and two-thirds believe the GOP leadership has not done anything to stop the Obama agenda.
For various reasons- mainly the ease incumbents get reelected- the caucus is only about 40% conservative or conservative-leaning.
The Leadership will have to reflect that, especially the Speaker.
You mention Jordan in a reply, he would certainly be a good Leadership pick. Several of the HFC members would be: knowledgeable in the ways of the House, with some political power of their own and very competent conservative politicians.
I believe it doubtful that any could or would compromise enough with the RINOs to win the Speakership though.