My reason for having offline storage is a holdover from my days of surfing porn in secret from my parents. While my dad never cared, my mom did; so whenever I got caught my dad would install some new filter or just turn the network off to appease my mom, but neither would actually check my hard drive for anything I saved. My dad wouldn’t because he didn’t care, and my mom couldn’t because she was terrible with computers. So while the Internet was off or until I could crack the latest filter, I had to make due with what I saved.
Also, any time we went on vacation, my parents wouldn’t let me use the Internet and I had to have some way of satisfying my porn addiction. And since I started collecting porn, I ended up also collecting clean images because I’m OCD and very habit-driven, and it just became another habit.