When I write a blog post, I want it to live on my blog, rather than a platform. I can thus invest my time thinking about how to make my blog better and backing it up, rather than having to worry about where my writing is, finding ways to export data from a platform, setting up persistent backups, etc.
A good overview of syndicating from your own website to social network silos:
The platform era is ending. Rather than build new Twitters and Facebooks, we can create a stuff-posting system that works better for everybody.
References and contributors include Cory Doctorow, Manton Reece, Matt Mullenweg and, of course, Tantek.
If you’re thinking about syndicating to Medium from your own site, this is probably the simplest way to do it—let If This, Then That take care of faffing about with the API.