The currencies of developed countries are pegged to the US dollar and so their reserve banks are just copying whatever the Fed is doing; their main goal is to make sure that the value of their currencies doesn't change too much relative to the USD. All countries reinforce the same economic distortions on a global scale.

Any evidence of that pegging?

The relatively stable exchange rates can be explained by entirely orthodox inflation targeting together with purchasing-power-parity pretty well.

The interest rates of developed countries tend to follow each other. Interest rates are one of the main mechanisms used to control the money supply.