I've written a lot of posts for the blog. I mostly find Medium a comfortable platform to post to, but am sometimes frustrated by its limited HTML. (And I know its lack of support for math has caused problems for others.) Further, using the WYSIWYG editor is mouse-intensive, so if I'm doing a lot of formatting or especially if I have a lot of links (like if I'm doing a topic round-up from the site), I instead write the post in HTML outside of Medium, drop it in my personal web space temporarily, and import it to Medium. That works pretty well -- there's usually a little bit of cleanup to do, but it's easy.
Embedding images is easy. Also somewhat necessary; Medium is very image-oriented in how it presents posts, whether on the blog front page or in a feed. So you've pretty much got to find some image to include, but that's probably good for us.
Posts on Medium can have tags (recently raised from three to five). Those tags are global to Medium; if you click on the "fiction" or "space" or "RPG" tag on one of our posts, you'll see fiction or space or RPG posts from all over the site. That's good in that it broadens our reach a tiny bit (and gives our readers other related stuff to read), but not so good if we wanted to cultivate a set of tags just for our blog. The scope for a tag (and its name) is all of Medium, not just Universe Factory.
I've made a few support requests at Medium. They've been reasonably responsive and they fixed my problems (sometimes on the second or third try).
Something I consider a key feature is that we can have many authors, who can submit work once or on a regular basis or anywhere in between, and a few editors (not just one) to manage the site. Distributed workload and distributed access are important for a community-run site.