The language of your statement reveals the problem (sorry for being deconstructionist...)
There is very little that the Constitution prohibits -- that's not how it's constructed. It's not designed to blacklist certain governmental powers.
Rather, it starts from a perspective where all rights belong to the people, and the government may do nothing. It then whitelists certain powers as the people have decided to vest them with the government. That is, the government can do nothing other than the things the people have enumerated for it in the Constitutions (particularly Article 1 Section 8).
That people think of government power in terms of whether it's prohibited by the Constitution rather than whether it's allowed by the Constitution reveals how far away we've gotten from understanding how it was intended to work.