It's a distribution / curation thing, like writing an Op-Ed for a magazine instead of publishing it on your blog. Either way you get the word out, but by ceding control to the magazine you gain access to a wider audience, unless you are in the 1% of bloggers who are a destination themselves (like daringfireball.com). Even Krugman "blogs" via the NYT instead of on his own domain.
Both ways are valuable, of course. Just providing the counter argument.
My comment was directed at the question of why someone would share copyright of their written work with an external party. One common answer is the distribution channel and pre-packaged audience. In that respect, NYT and Medium provide similar function.
Medium sends out an e-mail with hand selected stories every week though and I find myself reading a couple quite often though. That's much less likely to happen with your own blog.
Yeah, Medium is tantamount to the blogging equivalent of an online petition in 2014.
Lots of Open Letters. :)
I wouldn't mind if they disrupted away the opinion columns and letters to the editor in newspapers, though. Better to fit it all in one place to ignore.
For a distribution/curation thing, I just prefer everyone write their own articles/content on their own website, and then have something like Hacker News, Retweets, Kottke, FB, Flipboard, etc...to float the good things to the top.
EDIT: the only time I've ever gone to Medium to read anything was when something surfaced on Hacker News. I don't really see it as anything more than another blogging engine.
Both ways are valuable, of course. Just providing the counter argument.