You really can't compare insurance liability to "Slop as a Service" liability (or however we want to describe the robot rental companies.)
Insurance is one of the most heavily regulated industries around. (This is US-centric, but insurance is heavily regulated in all advanced economies except, arguably, Florida.)
Most folks tend to think Regulated Industry means they can "get away" with less than other companies. And that's true in certain ways. But it also means they can absolutely do things that would leave them exposed to liability if they were unregulated. It ends up being both restrictive and freeing in different ways, and the details invariably end up being really complex, arbitrary at the margin, and enraging when it bites you. It isn't even all the insurers' fault - in the US every state has their own regulator, and the rules vary quite a bit. (Florida has very few.)
That's how you end up with home insurance that covers squirrel damage but not raccoon damage.
Which all means that the abusive behavior insurance companies get away with ends up looking a lot different than that in other industries. Each industry is its own special tapestry of grift.
This is more speculative, but I think we are gearing up for one hell of a moral panic over LLMs. Most recent moral panics have been legacy media creations, and they're captured by robot-money, so we won't see Fox or ABC running with it for now. But I'd give even odds someone does something spectacularly awful because their robot friend told them to* within the next year, and then there will be buckets of organic "won't someone think of the children" for demagogues to exploit.
*details and nuance won't matter