That’s a fair point.
The Speaker’s views however don’t technically matter (though they do) because his job is not to get his way but to get the caucus’s way.
The real job of the Speaker is to get his members re-elected. Not as cynical as it sounds, doing what the voters want gets them re-elected in a perfect world.
When two thirds of GOP voters believe the leadership has betrayed them, that is the result of not doing what the voters want.