The icons annoy me as well and it just seems like they're trying to be something they aren't.
Wow. I haven't been using FB much after dropping it from my phone. They are very similar.
Hiding content below the fold is one thing, but IMO not being able to interact with any of it without scrolling is bad design for a number of services, Twitter being one of them. For a Medium article, I am going to have to scroll anyway to interact with the one thing I am there for. It's tolerable. However, Twitter has a core status/update functionality that should be served, at least to some extent, by casual perusal. But, like you said, it seems like they are trying to be something they aren't.
They probably found the more you have to scroll, the longer you are on the site, which would be a positive signal leading to a negative experience.