The Warehouse is a power unto itself, apparently. It might be located in the "most powerful" nation on Earth at any given time, but that doesn't mean it is run
by the government. Otherwise, how could the Warehouse move
through the ages?
The US government would never allow such powerful artifacts to move to another nation of their own accord. Presumably the UK government did not want
the Warehouse to move to the US back whenever it moved. Again, presumably the Russians didn't want the British to have the Warehouse and its artifacts when it moved...etc, etc, etc.
Clearly the Regents rule the Warehouse and determine where it is safest and most secure through the ages. Their criteria may have changed and their relationships with the governments evolved, but the Regents aren't government agents.