Why would Putin and the U.S. government and the European Union get involved in the Fake Alien War?

 Because without it it is likely that the human race will go extinct by 2095 or 2050. Why?

Because overpopulation is the main cause of Global Climate changes we are experiencing now.

So, only through a drastic reduction in the number of people on earth (or tearing down all cities and moving underground) can the human race make it through the next couple of centuries without drastic population reductions worldwide.

IF the human race wants to live on the surface of the planet without moving underground then likely it can sustain only around 1 billion people at most for thousands of years.

So, in the early 1800s when the world first went beyond 1 billion people, global climate changes began slowly building up until now with around 8 billion people.

So, clueing the world into "The Fake Alien WAR" what better way to get people angry at aliens than to blame them for knocking up their wives and girlfriends and daughters? This is how it would begin for governments to bring up Aliens knocking up their women to get them angry.

So, Earth Governments are beginning to advertise the Fake Alien war in this way?

Maybe.