If I were hosting said Free Speech Drive, I would be oblivious to the contents of what my users host on their drives. I would not violate their privacy by spying on them. Their files, not mine.
If your site is widely used and you make it technically impossible for you see or moderate content in any way whatsoever, your site will become a host for real illegal content- not just the borderline examples I gave. As the comment above me notes, even 4chan removes CP. You place yourself in serious legal jeopardy with this decision
There is little legal distinction between a 'publisher' and a 'host', which I understand is part of the pseudolegal gibberish that's part of the 'content moderation is censorship' belief system.
If your physical storage unit is consistently used for illegal drug dealing despite several arrests there, and several warnings from law enforcement, then yes you'd probably be liable for that. If you had significant scale of illegal content on Free Speech Drive, then yes you absolutely do face liability. I guess if you think you have a clever legal argument otherwise, you're free to spend $100-500k on a defense attorney to make that argument after your public arrest, while your name comes up online for 'Illegal Content Provider' for all time
