medium doesn't allow you to bring your own domain, and that's fairly crucial. Both for longevity (can always point a domain at a new host, even if it's just a bunch of static files somewhere, if the old host goes away or becomes bad in some way) and identity: proper name instead of "yet another medium blog", which isn't exactly a signal of quality.

Still, there's tons of hosting options where that's not an issue. Running a VPS can be interesting and fun, but if you just want to host a simple site there's easier options that work just as well.