I agree, but don't think we can switch at this point in time. Hardcore religious voters make up a substantial chunk of republicans, if we splintered into a bunch of groups they would remain as one and dominate. We would need to also change over to proportional representation or whatever you call it when it's not a winner take all thing.
It seems like a system that could be easily gamed, we have enough pretty shitty people in our country that I don't think it would work. Just look at our last election and the aftermath. Those folks aren't going to have a problem with whatever unethical behavior, breaking up the party opposed to them seems like a recipe to fail.