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
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