What I write isn't interesting per se, but I don't want to depend on the bon vouloir of a VC-backed startup somewhere to keep a whopping 4.3kB online.
If I ever get over that hump, I certainly wouldn't want to make it harder on myself by hosting my own web server. I would want to write, not manage a server, with whatever complications that brings. That's what makes Medium (and others) attractive.
For the second part, I don't write regularly. I don't look for an audience tuning in every Thursday evening. I write when I feel like I have something to write about; when I learned something new and interesting that I want to share, that more people should (or might want to) know about.
This gives me a URL I can share with friends and/or post on sites, instead of telling friends individually or writing a post on a gated community like Facebook. It gives me some of history on what I've been doing over the years, showing a potential employer I've been doing IT stuff out of school as well (very useful as a young professional). It even serves to remind myself now and then, e.g. my IPv6 post[1] I fairly regularly use to check stuff like "what was the maximum address length again".
In fact, not writing regularly might be more useful to many potential followers. If you only write now and then, they can follow you without fearing their inbox/feed will be flooded, and posts are much more likely to be of quality. When deciding whether to follow back, irregular or semi-regular Twitter users are much more likely to get one from me because they are usually more interesting and not a day to day burden.
If the loss of control is worth the gain in ease, go nuts. Or if you don't really care if what you write stays online or under your control forever. Not everyone does. Twitter, for me: I really wouldn't care a bit if that service turned off entirely and I lost my archive of tweets. They just aren't that important to me. Or my Hacker News comments. They're interesting, but I won't be particularly upset when Hacker News finally dies off and they disappear. But my longer-form writing is important to me.
But I think people shouldn't be under any illusions about what Medium is. They're not a group of altruists trying to archive the world's writings for posterity. They're trying to figure out how to make bank. And if they don't, be aware of what will probably happen...
OTOH, if something like Medium weren't as bulky as it is and had more awesome CMS features like footnotes, I could totally understand somewhat-technical people sticking with them. It's less the self-hosting and -ownership that should be appealing, just how much easier it genuinely is to publish yourself for your own website compared to managing Medium.
Doing it yourself means it's as simple or complicated as you like it, and you can add whatever feature you want.
For instance, my blog displays a seasonal emoji next to the year: https://raw.githubusercontent.com/TazeTSchnitzel/blog/75d789...
It was almost embarrassingly easy (code is on there).
Really should write more content for it though.
Why does it break in Chrome on OS X, yet work in everything else?!
Medium's cool now, but it won't necessarily be in a few years. And it's completely within the realm of possibility that they will disappear entirely at some point. It happens all the time. Big sites that people have contributed mass amounts of content to blink out of existence on a very regular basis. Sometimes without warning or the ability to back-up data. But the best case, like Winer points out, is that any links in become broken, comments get lost, etc.
Your writing is yours. Own it.