Well in my system, all conservatives would move to the conservative region, and all Libs would move to the Liberal region. I'm tired of fighting the Left. I'm only 16, and I've already had enough. I can't take this every 4 years. Under my system, the South would be conservative paradise, the West Coast Liberal paradise, the Northeast moderate paradise, and the Midwest Libertarian paradise. Whatever you think of my system, I think you'd be foolish to say it wouldn't be better than what we have now.
I'll say it. It wouldn't be better than what we have now. Besides the fact that it involves uprooting tens of millions, if not more, of families and separating communities, it removes general group checks and balances within society and you could have run-away authoritarianism in all areas as more and more, demand for ideological purity is enforced. You can't even get 10 Conservatives (or Libertarians, or Liberals) to completely agree on what that means, let alone enough that you regionalised said belief systems.
The other thing is that what you are describing simply is a fantastical pipe dream. Unless enacted by force (which the implementation of would be just as impossible), human nature is we won't uproot our families or our communities to join people who happen to have the same political philosophy.
Politics also isn't the only thing that divides us. What about religious differences? What about differences in climate preference? What about just not wanting to be around like minded people all the time? Challenges to our belief systems is what makes us grow. Constant differences around us making us adapt to how we interact is part of human (and all of nature) evolution.
It seems you've gotten to the point where your world revolves around politics, which is understandable because politics gets into everything. But that also gets you in the trap that government, of any sort, is the be-all, end-all. You are giving it too much power. The more we stop looking for any centralized, government based solution, be it Conservative, Liberal, or Libertarian, or anything else, the better off we'll be.
Too many people stopped living their life as if politics isn't important- which is exactly what the political class wants.