I think Medium makes incremental improvement(s) over some alternatives. I'm not sure if the sum of those improvements will mean Medium will turn a profit, grow or survive, but here are a couple of thoughts:
Medium is content-first. All blogs should arguably be content-first, very few are. Most wordpress blogs a) look like crap, b) obscures content, and c) renders slow, in order to accommodate the design that contributes to a) and b).
I'm not a writer, but from what I understand, the back-end is also content-first, writing first -- simple, elegant, no clutter.
The lack of theming is a bonus. Just as design/layout of an essay in New York Magazine is largely out of your hands, and taken care of by the publisher, so it is with Medium. Evidence suggests that the vast majority of writers are better off that way (see point above).
Ghost and many of the static site generators offer similar benefits, but with some caveats: they all need theming, and I'm not sure if any of them really come with something that in sum is as good as/better than Medium. Personally I think even Medium is a bit heavy -- but it is way better than then current mess that is Blogspot.
If your goal is to write/publish and not worry too much about design/layout you could do a lot worse than Medium. Many do.
I wouldn't be surprised if Medium differentiated/launched curated sub-sites/"magazines" that featured content from Medium. They could have some premium stuff that is authored by only paid authors, mix and match, and have a X articles/month-for-free model a la New York Times etc.
If the can get a large number of writers, and a large sub-section of good/great writers -- monetizing shouldn't be that hard. I hope. And I'm guessing that's what the investors hope too. In fact, I wouldn't be surprised if Medium turns out to be one of the first "native digital" publishers -- embracing the strengths of digital distribution, rather than fighting it. Eg: maybe people are willing to pay for content, and one can simply rid oneself of the dependency on advertising.
We'll see.