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 I rent out a physical storage unit to you and you use it to run a illegal drug dealing business out of it, would I be liable for that?
I suppose not, which shows that the laws in regards to hosting stuff are off and those should be changed.
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
It is easy to be an internet tough guy, how about you actually start a simple file server with no restrictions and see how it goes?