The main thing I miss about "old" internet is personality. With Twitter, Facebook, and Instagram you'll always have the same boring page design around your posts no matter who you are. Sure the content you post will get your personality across fairly well, but just like with art it's not only the painting that matters, but also the frame.
It's one of the two main reasons[1] why I vastly prefer Tumblr over the three aforementioned sites. It lets you create a page that's your own to customize how you like. And that makes it much more personal and interesting than Twitter and Instagram imo. I really wish those sites would start letting users customize their pages more than just by changing their profile pictures and header images.
[1]: The other being the ability to view all posts from people you follow in a sequential order instead of having some algorithm decide which posts you should see.