You can use someone else’s software, but still have your own “platform”, if you’re hosting it from a domain name you control and are able to easily take your content and traffic with you to another tool or host at any time. You don’t need to go full-Stallman and build your own blogging engine from scratch on a Linux box in your closet — a Tumblr or Squarespace blog is perfectly fine if you use your own domain name and can export your data easily.
It’s unclear what Medium’s plans are, but so far, it looks like they’re going slightly more for the content business than the publishing-tool business. That’s why “Medium” is the prominent brand everywhere — the URLs, the layouts, the titles — instead of quietly settling for a little “powered by” in the footer and letting the author keep all of the attention.
Treat places like Medium the way you’d treat writing for someone else’s magazine, for free. It serves the same purpose: your writing gets to appear in a semi-upscale setting and you might temporarily get more readers than you would elsewhere, but you’re giving up ownership and a lot of control to get that.
Whether it’s worthwhile to you should depend on whether you want to establish yourself as a writer, whether you want to get paid for it in some form, and whether you can get an audience elsewhere on your own. Plenty of people can answer “no” to all three, especially if they do something else extremely time-consuming for a living and want an occasional place to write, but don’t have the time or inclination to try building regular audiences or become known for their writing. People who sometimes want to write, but never want to become even part-time writers.
But if the answer to any of those questions is “yes”, and you have any aspirations of building your own audience, you should consider whether it’s wise to invest your time and writing in someone else’s platform for free.