I don't think your parable of the mechanics without tools makes for a very good analogy with the problems of politics. In your story, it seems clear that if a mechanic came along who had the skills and equipment to actually fix cars, he would rapidly achieve success and drive the ineffective mechanics out of business. The problem of politics is that the nature of the system is such that it does not reward competent policy making but rather rewards competent politicking. The two seem to be only very loosely correlated.

If the desired outcome is good policy then the problem is not how to create greater policy making competence in politicians, or even to educate the public in how to recognize greater policy making competence in politicians, but to restructure the system so that competent policy making is rewarded. The fact that such a political structure is rarely if ever observed in reality suggests to me that good policy is not actually the true desired outcome of political systems.