It's very shocking to me that you would reply in the affirmative.
I think you're saying that companies who host generative AI web services, ought to be legally liable if the ephemeral generative content is illegal.
In your mind, should AI companies try and engineer protection from this huge legal risk? It seems criminally insane for a company to host an AI if they're going to be legally liable for the ephemeral daydream content. You should be shorting goog, meta and msft at the very least, because I make their models generate illegal content every night before bed