Yes probably some things aren’t supposed to be in the internet 
But I don’t see the point in a completely anonymous nostr 🤔

But what if nostr was the common thing in the world, what about communication? 
Would we continue communicating privately with our friends on other apps like simplex or telegram or phone number?

or via nostr? 

 Nostr is 100% public, with all that that entails. I wouldn't attach my Nostr account to my identity, for that very reason. 
You can always have anonymous accounts that you could use to establish contact with other people, then selectively reveal your identity to them.