I’ve written a few things on Medium (not paid) because I liked the experience of their writing tools, their statistics, and their reach. I think two of the three items I wrote became featured and had several thousand reads. It’s a wonderful way to write and a wonderful place to post.
But it’s not mine. It’s theirs.
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, Squarespace, or WordPress blog is perfectly fine if you use your own domain name and can export your data easily.