I do not know those final 2, but Love is an Open Door is not a Villain song. It's a love song. They do not share the same role. Also Hans is a terrible twist villain.
Super Mario Boards
Paper Mario
I think that's because the reveal that they're a villain usually comes at the climax, so unless they do their villain song AS they're revealed as the villain, there's not really a good place to have the song.
Mario Fan
That explains it, but it doesn't make it any less sad.
I'm the friend you need sort of counts
We Will Stand For Everfree