Google+ nailed this perfectly. You could place connections into Circles, and a post could be shared to specific circle(s). It let teenagers be teenagers, allowed professionals to separate their personal life and maintain a professional appearance, and so on.
In reality we do maintain separate personas for different groups of people we know, and it's ridiculous that no social network reflects this. The closest anyone else has come to this is Reddit where you can use multiple pseudonyms, so someone recognizing your posts/comments on one account does not get access to all of your posts/comments.
Also I'm pretty sure you can create lists of your friends and share certain posts or images with "everybody but X, Y, and Z" or "X and Z only" where [XYZ] are either lists or specific friends.
Even if it had been implemented in its current form 5 years ago, filtering post audiences still seems to involve a level of added complexity not readily tractable for your run of the mill user.
It used to be a bizarro town-hall of people I knew posting comments, photos etc. with each new post jumping to the top of the queue for people to pay attention to in "real time". It felt involved.
Now it just seems to be (in between all the shared memes and dodgy news articles) the more "active" posts popping up as a priority, which makes it feel more static to me. I liked seeing the posts with no likes as much as the high activity ones even if I wasn't going to like or comment on it myself. I wan't to see everything in order.
It's not very dynamic anymore.
I know you can still change the feed to chronological, but if most aren't doing that, the point is moot.
I use it for events, otherwise I'd have deleted it years ago too.
It was cool at first because I actually spent time with my "friends" on there, or at least saw them on a daily basis at my small high school. It's changed in a couple key ways over time:
1. Family joining Facebook. It used to be a funny place I could goof around with my friends, posting whatever I wanted. Now I have to filter everything I say because my grandparents can see it. I concede that that's probably not a concern for many people, but I noticed the "vibe" changed significantly when Facebook's popularity grew beyond high school/college age people.
2. Sharing. Virtually everything on my timeline came from pages that post short "viral" videos for people to share. No one was posting anything unique or interesting. It was like a heavily bastardized version of Reddit without any interesting content. Anecdotally, this content seems to appeal to older people, who don't know of ways to see more interesting content.
Privacy concerns aside, those are the main reasons that I no longer care about Facebook. I deleted mine 6 months ago and I don't miss it at all.