Because we have structured society and our culture in such a way that some people can only feel safe when inside a small thick wall cell with the door locked behind them. That's terrible though, my proposition is to invert that, what would allow people to sing in the streets without any fear of judgement, and use that as a basis. Privacy as an idea suggests "let's put more doors with locks" when in fact that doesn't help at all. It doesn't address the problem that necessitates those doors with locks to exist.
I couldn't agree less. It's not a function of social structure or culture, it's an innate human trait. Your proposed society is to me simply a dystopia where no one is free to be a complete human being.
Separately, privacy and secrecy are related but distinct things. Telling me that you sing in the shower is a different thing than inviting me in to see and hear it.
