Part of mediums problem it's that it's so restrictive.
It is an unfortunately restrictive platform; I'm still a bit surprised at how popular it is for writers.
I think the attraction is it's close tie with Twitter (for some reasons, many writers seem to be in love with twitter; I do nothing there but curse and spoil movies), and that it's "easy." I personally run a small website using Ghost, that's all the functionality I need. However, for some articles, I can publish them "anonymously" (through a fake Twitter/FB account) to prevent blowback on myself (for instance, I could publish an article on suicide and not link it to my name, to avoid the taboo that follows the subject around).
That writers love twitter confuses me even more than that some like medium. Perhaps it's just because I use twitter as a glorified RSS feed, but IMO conversion/discussion is horrendous on twitter. In any event, I too use a Ghost setup for my own blog but I've never had the itch to write something that could blow up. I can see the value of something like Medium in the case that I would, though.
I agree, twitter does nothing but irritate me. I don't think I've ever seen anything there "of value," and if something does pop up, you can bet it will make its way to about 27 different blogs in a matter of minutes. Twitter has been, for me, just another source of stress. Over the last two years, I've flipped flopped a bit. I completely removed Facebook in favour of twitter, and since January, I've completely removed Twitter in favour of Facebook. Honestly, if three specific people would find a way to communicate that didn't require Facebook, I wouldn't be there either. Textual communication is something I almost completely detest. Not long form writing, but actual "chats" such as Facebook Messaging, Twitter conversations, etc. There's no emotion, no social context, no clues or any way to read what's going on. This has actually made the period a notification of anger. This is part of a much longer rant, but I'll simply leave that point since it's not relevant. Ghost is nice, it's easy to manage and allows me to write. I've never written anything on my site with the thought that it'd "blow up." I think the piece that got the most reads was when I "came out" and even that was only about 30 hits out of 120 Facebook friends and 80 Followers (that post doesn't even exist anymore). I'm lucky to have 10 reads of anything I write, unless I post it to another site (which I'm always hesitant to do). I think you're right on the money with the "blow up" draw of Medium. That's the only reason I find it attractive, the layout and aesthetic is completely achievable through CSS on even the simplest blogging platform.