Even if you own the copyright to whatever you posted, it's not in most site's interest to certify that to enough of a degree of confidence to allow it. I think back to issues Youtube has had in its own attempts to police Copyright, which has led to widespread abuse, and absurd situations like composers being hit with strikes for uploading music that they composed.
I think that argument is more or less well understood, and I think the logic transfers over to use of powerful tools to police copyright infringement.
We can't anticipate how those tools will be abused in idiosyncratic ways by flawed political systems, and we shouldn't enable vast enforcement powers without building in the same checks against human abuses that are part of democratic systems.
Even this concedes too much. Suppose machine learning gets really good and it became effortless to monitor posts for infringing content? We'd still be deploying tools that control, constrain, and chill internet activity in haunting ways, and that's not a direction we should go.
To me, that is the problem, not the practical difficulty of implementing the rule, which implicitly admits that it's right.