An attack like this doesn't really need the exploited computers to run inference, do they? If I was an LLM bent on destruction of the internet, I'd be writing programs to run on each computer, not turning each computer into an LLM itself.
A few programs to break in, install themselves and remain asleep until they are needed, another few to spread through grabbing every OpenAI, GLM, whatever key, another one to remain asleep on computers (whether hosted or desktops) that have adequate GPU, etc.
More to the point, so many people in this thread are making completely contrived and outlandish stories up about how AI might try go ruin our lives without any evidence backing them up in any way. It is hysterical. This is the most important technology in our lifetimes and people want to freak out and turn it into the next nuclear power, with progress banned in all but name.
But yeah you're not going to be able to shard out the terabytes of Fable weights that are needed to run inference without addressing some fundamental physics problems.