Yes, Austria is right to purchase the home in which Hitler was born and grew up. The country has had a lot of problems with neo-Nazis going on pilgrimages to visit the home and pay homage to Hitler. It is right to destroy the home so that hate groups do not have a focal point.
The Austrian government recently announced that they were planning on destroying Adolf Hitler's birthplace. This is an excellent idea because his birthplace could attract neo-Nazis who are interested in making a pilgrimage there. By getting rid of Hitler's birthplace, neo-Nazis are prevented from having an icon or further sources to make them more fervent about their beliefs.
This house serves as a reminder of the horrors committed by the Nazi's and if anything reinforces the memory that what happened during the third reich must never be allowed to repeat itself. Neo Nazis will emerge with or without traces of Hitlers life still existing irregardless of if someone tried to erase to all via demolition/ destruction.
No, Adolf Hitler's birthplace should not be destroyed. There has been so much destruction associated with the Holocaust and it should all stop. Healing should be done in other ways than continuing to destroy places and things in our society. While Adolf Hitler was born there, it doesn't mean it doesn't deserve to still stand.
I do not understand why you would remove the house of a man who was the leader of one of the most prolific countries in the 1940s. He was a war veteran and greatly admired by the people of Germany. Sure he committed many "evil" acts (I would not call them "evil" only "inefficient") but that does not take away from his legacy.
Under no circumstances should Adolf Hitler's birthplace be destroyed. Simply removing such a structure does nothing to erase the history of the that Adolf Hitler was. This is somewhat a kin to removal of Confederate flags here in the United States from government buildings. Those are merely symbolic gestures they have hold no water and do nothing to change history. Feel good measures only.