The "companies want this" argument is irrelevant. Even if true, it doesn't make prior restraint constitutional. The government can't delegate its censorship powers to willing corporations. If companies are worried about liability, the answer is tort reform or clarifying safe harbor provisions, not building state-mandated filtering infrastructure.
On whether AI output is the company's speech: The First Amendment issue here isn't whose speech it is. It's that the government is compelling content-based restrictions. SB 53 doesn't just hold companies liable after harm occurs. It requires them to assess "dangerous capabilities" and implement "mitigations" before anyone gets hurt. That's prior restraint regardless of whether you call it the company's speech or not.
Your argument about LLMs being imperfect actually proves my point. You're saying mistakes will happen, so we need a framework. But the framework you're defending says the government gets to define what counts as dangerous and mandate filtering for it. That's exactly the infrastructure I'm warning about. Today it's "we can't perfectly control the models." Tomorrow it's "since we have to filter anyway, here are some other categories the state defines as harmful."
Given companies can't control their models perfectly due to the nature of AI technology, that's a product liability question, not a reason to establish government-mandated content filtering.