"I think, therefore I am" or "I doubt, therefore I am" has only opened up unanswerable questions. Which isn't all bad in itself because the exercise of thinking and wondering is food for the mind-- unless one comes to a nihilistic conclusion and resolves there's no point to anything and therefore does nothing.
But philosophy so rarely answers anything definitive except that the whole of philosophy is a statement-- a reflection on human nature. There are more answers in philosophy about the nature of a human being who questions his own existence, but it doesn't answer whether he exists or not, or even why he exists. It gets him to ponder and exercise his cognitive boundaries. And his conclusions offer him information about his own self.
I sometimes see philosophy as an artful exercise. Something which can be beautiful or ugly and offer insight into each of us. But as for answering the universe around us, or even dilemmas of the corporeal body vs. the mind (or spirit), it holds no answers. Only more unanswerable questions.
As for politics and religion, these, too, are constructs and reflections of ourselves. They can offer guidance, but never answers. Therefore, they must be treated with caution and reverance because we give them the potential to destroy.
As for the separation of all three, I don't find the idea one to entertain. They are interwoven due to the simple fact that they are, all three, conceived in the human mind. And despite its many factions and divisions, the mind is too much a gestalt to remove or rescind any one part of it. All of these inventions of cognitive fancy are products of unlying mechanisms and functions, quite a few which, I have no doubt, lead to the creation of philosophy, religion, and politics. To remove one without removing the other two (politics perhaps a little less so, since it deals also with interaction and not just the single self) is very hard for me to conceive...