The question is flawed.
The premise is not "what authorizes a cop shop to exist" but "what prevents a cop shop from being authorized."
There is no constitutional mandate one way or the other. The intentions and omissions of our Founders is irrelevant. A representative republic can either make a cop shop, or not. Or, the representative republic can dissolve a existing cop shop.....even today. The views of that representative republic's citizenry must then be addressed, one way or the other.
Anyone who values the Constitution, and their state constitution(s), must accept the fact that the federal AND the 50 respective republican forms of governments have, and by extension the citizenry, approved of and desire a cop shop to be close at hand.
If you don't like cop shops work within your state to dissolve them, or the offending cop shop......and please let us know how things are going on that front from time to time.