The word "Reich" has been given a bad rap ever since the Nazis...perhaps even before that. It's an ordinary German word which simply means: kingdom, empire, or realm. It could also be taken to mean "commonwealth". When used as an adjective, "reich" means "rich".

The united realm in German would be der vereinigte Reich, for instance. How is this any different from calling Great Britain "the United Kingdom"? Reich is not a word that implies anything evil, but to call present day Germany the "Fourth Reich" in today's post-WWII political climate is to strongly suggest that present day Germany is like the Nazis...not a fair or useful suggestion, in my opinion.

Are they playing power politics? Sure. What great power does not? They all maneuver to seek financial and political gain.