Instagram almost works that way. Sometimes you can see a bit of content, but not much, even if you have direct link from friend.

I do not have account - just of the reasons you mentioned - I cannot justify if there’s anything interesting for me.

I don’t know, it seems to work for Pinterest.

TBF nowadays the move has a certain logic. By keeping your content private you keep it away from search engines and LLMs. Twitter does not rely on search engines to drive traffic to it, and it’s a large, already established platform (current efforts to drive it into the ground aside). If any platform should be able to go private, they should.