That is partially true. The Hungarians were generally perfectly fine with the last Hapsburg being King of Hungary. The Allies were not. Since no faction could agree on a replacement King, Horthy was elected Regent.
"Louis, Louis. Harry, Harry. Your my candy King..."
Ha. I always liked the Bourbons. They might have remembered everything and learnt nothing but you can tell that they really like being Kong’s of France and latter Spain and the Two Sicilies. The Hapsburg did not seem to enjoy it that much.
The first Hapsburg Holy Roman Emperor was Rudolph in the late 13th century. He was picked because of his obscurity. To this day, school children sing about Rudolph the Red Nosed Emperor in Austria. They didn’t secure the throne permanently until Maximillian I.
The Stupir Mundi was Hohenstaufen. Same with many of the others.