1) Don't show posts from people I don't follow 2) Don't hide posts from people I do follow
Facebook gave up on that years ago, and that's probably one of the reasons I've mostly stopped using it. Now Twitter is following in the same footsteps. More and more I'm getting posts showing up in my Twitter timeline that are not from people I follow and weren't retweeted, they are just "person X follows this account, so here's a tweet from it". No! If I cared, I'd have followed it myself.
And now all this talk about showing "important" tweets that Twitter thinks I "missed". Stop it! You don't know what I think is important. Again, this is what drove me away from Facebook.
(Not even talking about ads/"sponsored tweets" here, though that doesn't help either.)