You can totally self-host your own VPN, a lot of folks will do that so that they can access their home lab remotely (without having to open ports or set up a reverse proxy).
That said, self-hosting kind of defeats the purpose of using a VPN service if the goal is to anonymise web traffic or bypass regional restrictions/ content blocks.*
* Technically you could use a hosting service and host your own VPN in another region, but it's probably not going to be cheap, and it's kind of a stretch of the self part of self hosting.