Nope, will never work. ANY “exit exam” must be standardized to be valid. To be standardized, someone must control. If the states, it will not be standardized.
There is no way to keep this out of the feds’s hands, which is to say, the elite academics. Trust me. I’ve just retired from almost 40 years as a college prof and I’ve seen the way such standards come into existence at every level-—elementary, high school, college. You would have PRECISELY the Marxist, non-fact based questions dominate.
I understand your point, but there's really no way to incorporate political philosophy into chemistry, engineering, math, and a variety of other disciplines (obviously, economics etc. would be more susceptible). The bigger danger, as I see it, is that the questions would most certainly be solicited at least partially from faculty at different universities, and I have no doubt that some would teach specifically to their questions in order to give their students an edge on the exam. That said, there are ways around this (e.g. random computer-generated questions).