What you're espousing has already been done. Just get up any Sunday morning and watch all the cars file into different parking lots so different Shamen can tell different folks very different stories about something no mortal could ever know. Not only that, but they'll say it with perfect conviction that they've turned over every rock and dispelled any questions.
Why do the religious and the political share so much bath water?
Because making people believe such BS takes a Sky-daddy and his evil brother Satan just to shore things up.
That's the Republican Party intermingled with their favourite toy.
Better yet is to do away with political parties and let those that wish to be elected be elected based on their ideas, not by how much money they can raise for the party or by how much a party can spend to get them elected.
Wouldn't that be a novel idea? Eliminate the obligation to adhere to a party line and be judged by what he/she believes what would be best for the country. No more House or Senate majorities. Just law, bills and nominations approved by merit, not party doctrine.
Free thinkers instead of party adherents. No more districts to fight over, just at large elections.