I think there's a full spectrum you're missing. You can own something with other people, and your level of control can be continuous, not discrete & binary. For example, my public library is funded by my local government, which I can influence with lobbying and voting. I can join the board of the library, and I can just go and talk to the librarians in charge to influence their decisions.
In an individualist consumerist mindset things are pretty stark : full self-hosting or full submission. If you reject that mindset there are many more options.
Let me remind you of the open source credo about free as in freedom not free beer. You are right that there may be exchanges or compromises at play, but it was a bit shocking to me when talking about what is essentially the digital commons that no one mentioned a library, which exists.
I'm also saying from a practical perspective if you want to stream movies without giving money to big tech, you can literally do that tonight with a library card. The infrastructure already exists.
Nominally, yes. In terms of that meaning anything, no. The benefit of ownership is not exclusivity, but control. If the library doesn't have a book (or other piece of media, of course), I have no power to influence them to get it despite that theoretical ownership. If the librarian decides a book is offensive and removes it from the collection, I have no power to influence them to keep it. I have to live with someone else's decisions about what the library does and does not contain, just like with a commercial service. So my nominal ownership really means nothing at all.
Either you own and control something, or you do not, there's no third option. A best, you can outsource your stuff piecewise: run your own software on a cloud VM, or bring your own furniture into a rented apartment, or give a valet the keys to the car you own for parking, etc. But there's always some relinquishing of control in exchange to some other aspect of efficiency / comfort.
It's also easy to mistake what most people want for what everyone wants, and miss an important market.