What would that do to the Speaker position?
If you're familiar with the British/Canadian/Westminster system, I'm guessing the speaker would play the same role - that is, a largely functional position that helps facilitate the parliamentary process without taking a very active role in the politics. In this case, the speaker wouldn't be the most prominent house member from the majority party, but just a respected congressperson from a safe seat who is very knowledgeable about the procedural aspects, and has good relationships with both sides.