I think this would almost be possible. If you wanted to build a completely private blog that only you have access to, you could build a blog system that just uses Nostr direct messages as storage: https://github.com/nostr-protocol/nips/blob/master/04.md. The problem is I am not completely sure how you would share certain things with friends but I do think it might be possible with enough time to put into it to think about how to do that. Probably a few clever solutions ready to be put into action.

Nostr itself isn't anything more than a protocol, so an app or website would need to be built on top of it that would allow you to do this.

It would be cool to see such an app or website.

Just got done doing research on this. https://github.com/block-core/blockcore-notes might be the closest app to what you are looking for right now. Here is their main site: https://notes.blockcore.net/connect.