But recently Medium discontinued support for custom domain names. And if you can’t even have a domain name for your blog, it’s clear that Medium is much less a true blogging platform and really just a social network for long-form content.
I confess that I missed that Medium had done that. And yes, it does matter. If you can't use your own domain, you don't own your own traffic, and that means your site exists purely and solely at the whim of Medium. You can't shift elsewhere and take your tarffic with you, because the moment you shift URL the existing traffic disappears.
If anything, Medium is on its way to becoming one of the biggest publications online, rather than actually being a platform.
The need to own and maintain your own domain is critical to long-term publishing on the internet — and it's something all too often forgotten in the platform publishing age.