Doesn’t what you descript already exist? Mastodon does all of this.
Besides, the Fediverse and ActivityPub is particularly a social network. It’s basically a web of json-ld documents. I expect my posts and data to federate across the entire network for the Fediverse to see, as long as I set my audience to such per post. This is already way better than Facebook, for example, which actively non-consensually scans my phone for contacts, tracks my location 24/7, etc.
Usually, people asking for privacy on social networks confuse privacy with anonymity or pseudonymity, which is an actual problem. Is this what you mean?
I wrote an article specifically for the purpose of introducing the Fedivers to potential newcomers. Perhaps you’d like to share it.
https://torresjrjr.com/archive/2020-07-20-what-is-the-fediverse