Also, when I notice a particular book it can spark a memory (even about the surrounding context of when I read the book) which are small but nice moments.
I'm not sure I'd feel the same about DVD / Blu Ray boxes though. I'm pretty sure the VCR boxes I used to have were just kept in a closed-door cabinet and I barely looked at them unless I wanted to watch a particular film.
The further your timeline goes into the future the more sense owning your media makes. You might not want to rewatch this movie in the next ten years, but what about the next thirty? Fifty years? Inflation will only make subscriptions more and more expensive. Thirty years ago a yearly salary of $40k was the same as a yearly salary of $100k now. It's funny how so many people think they earn more than their parents did, when in reality they earn way less. And that won't get better in the future. Maybe you won't even have enough money in your retirement to afford a subscription.