The main difference between each of those scenarios and the one I describe is that we have words to describe them. From your post: freehold, leasehold, buy, rent, loan (and I'll add: mortgage). You don't need to read the fine print to know that these are meaningfully different.

I'm on board with the idea that there's a lot of arrangements in between full ownership and pure rental, as long as we have terms to describe the meaningful differences.