> there is no great solution to limit the visibility to certain audiences

There's an important sense in which you are very wrong here because nothing on the internet is actually hidden. Everyone can see everything regardless of the visibility you think you've put on something.

But there's another sense here where audiences do tend to self select into groups and do tend to see and (crucially) engage with things in niches. The early web was very much this first kind of social network where we all could go and read random stuff but we all found niches that we fell in love with. This gained more structure (and convenience) with web forums and then perhaps MySpace and Facebook and other social media added even more structure (pictures only with Instagram, short messages with Twitter, video on YouTube, etc). The structure has also morphed so that these platforms all start to look a bit like each other too.

All this to say, for the "old web" to return, it would need to be as "structured" as the one we have now but give us back the freedom to build whatever really cool thing we wanted. I think the only way to do this is with progressive enhancement of some kind.