There is no political advantage to holding the Armenian Genocide in any regard. The great powers decided at the 1919 Paris Peace Conference that nations like the Poles and Czechs would be granted self determination and nations like the Armenians would not, and that was that. On the other hand, there are lots of political advantages to throwing the Armenian Genocide under the rug, usually to appease Turkey. One of the first being that the Allies wanted a powerful buffer state with the USSR, so it made more realpolitik sense to form a friendship with the Turks and do nothing about them exterminating the Armenian nation and turning their lands into living space.

The only other Central Power nation of significance was Germany. The Germans were fully aware of the genocide and supported it. Lots of historians argue the Turks wouldn't have done it if Germany had been against it. Both wanted to appease the other. Germany was also considered by far the most anti-Armenian country in Europe at the time. Lots of newspapers were very anti-Armenian and compared Armenians to Poles and Jews. After the war, a lot of the Nazis came to idolize Turkey for expanding through ethnic cleansing and getting away with it.

Still, it's worth noting not all Germans supported it. A lot stationed in Turkey became important witnesses. Johannes Lepsius was an important German intellectual who sympathized with the Armenians, became the first chairman of the German–Armenian Society, and documented the genocide. But again, German intellectuals were for the most part pro-Turkish and had no problem justifying the genocide.

For more information you should read "German responsibility in the Armenian genocide" by Vahakn Dadrian and "Justifying Genocide: Germany and the Armenians from Bismark to Hitler" by Stefan Ihrig, which is only a year old.

Here is also a great summary:

https://www.facinghistory.org/resource-library/german-connection