What we must fight for is for legislation equiparing Bitcoin explicitly with ISPs in this aspect (everybody in his jurisdiction).
ISPs are not storing and distributing illegal material, though, right? Such as copyrighted movies or much, much worse..?
I'm afraid that no modern cryptography can solve that problem - if somebody is able to read the data, even the uploader himself, then he can make them accessible for others, too, if this is his intent.
Should we not aim to make it as hard as e.g. Grin is making it (or maybe even doing better than that) to abuse the system and put Bitcoin nodes at risk of legal trouble, just because it is still possible there, at a much lesser extent?