I've only rented a storage unit a couple of times but for me there were two factors: one was knowing the history of everything that was in it. And the other was that I had chosen those items.

I liked knowing that nothing was damaged in ways that weren't easily visible, like something you bought used might be.

And I don't enjoy shopping so trying to get something just like what I had is/was difficult. And it's getting harder: manufacturers change models at an incredible rate. You have to read reviews all over again, etc.