People use Medium because it's the easiest way to write some plain text and have what you wrote look decent in the browser. That's all it comes down to.
That's not plain text, it's HTML. It's a total fiddle to write by hand (lots of angle brackets), and as you say you then have to find somewhere to host it.
But it also doesn't look as good as Medium. If browser makers were willing to be progressive and act as user agents, like they were originally intended to, then the two would look very similar. Unfortunately web browser text sizes haven't kept up with increasing screen density and so we have point-size inflation instead; the complete lack of margin also makes for a struggle when reading (though I do think Medium has gone too far in the other direction lately). Medium's link styling is less obtrusive; conversely code blocks on motherfuckingwebsite-style sites aren't visible enough. Image sizing on motherfuckingwebsite-like sites is also all wrong (they're sized to pixels rather than to anything meaningful). A lot of sites look worse than motherfuckingwebsite, but Medium is an improvement IMO.
I've always found Medium to only become readable once I use Firefox's reader mode. The interstitial, the aggravating headers and often footers, the utterly useless sidebar icons.
Their styling is unobtrusive, but the result is something that leaves me thinking a designer needs to be shot for working far too hard to justify their pay.
Pretty much. Writing markdown with jekyll is too technical or not WYSIWYG enough for most people who don't want to touch a command line, and running your own ghost/wp/etc blog is too much for the average person to do without using ghost.org or another pay-per-month hosting service.
The irony is that people go to medium because it's kind of .. expected somehow? And looks more authoritative?