Of course services like the registrar need protection here too. And certain false copyright claims probably need consequences as well. The legal industry servers no function here.
Also, it would be legally trivial to make the user accountable for the offense, not the whole of itch.io. Sure, there would be problems here as well, but there is not large barrier to not have a parasitic legal industry and have those responsible that actually commit the offense.
The problem of enforcement cannot be put on the back of the platform itself.