The Republican Party is not dead. Far from. Put yourself in the shoes of Republican voters. The truth is that they do not have anywhere else to go. If our two-party system is like good cop/bad cop, and if we say that the Republican Party is bad cop, do you really think the Republican voters are going to run toward good cop all of a sudden? No.
The United States is probably the most anarchistic nation on the planet because the two parties do not represent two factions in opposition to each other, but one faction that wants more government and one that wants less government. Those are not oppositional forces under normal conditions. These factions are ideologically alien to one another.
Together, neither succeeds. Together, they are mediocre in their outcomes. And that may serve the Republican ideal of having less government, less trust in government.
If both are seen as cops, then one cares and the other does not give a hoot, not even when cops are supposed to serve and making it better for all in society. Naturally, third parties of special interests do benefit from a more anarchistic government than from a smart and benevolent government because of less regulation than elsewhere. Either way, the Republican Party benefits (and their special interest groups).
I understand where you are coming from, but your thinking is based on our being a democracy. We are not. We are an 18th century two-party system and the political reality is that of good cop/bad cop. The Framers really did frame us. The Republican Party may have to reinvent itself, but it will do so on the grounds of not wanting to organize our government the best way possible.
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Promoting one of my latest articles here:
https://medium.com/the-national-discussion/and-the-winner-is-the-losing-party-c683c1d739e5
It sounds weird, but it is actually true that the biggest group of voters are the losing voters in our system. In the other more modern version of democracy, there are no losing voters because all voters get the one they handpicked themselves.