Even for domestic robots people don't care, see just about every cloud connected smart vacuum robot and the numerous data leaks
And for companies, most of them are fine using SaaS and cloud based hosting platforms, so why would it be any different for robotics?
Sure there is the latency argument, so at least something doing very short term decision making needs to run on device or at the edge, but for most task the end to end time is in the single didit seconds to minuites, so the extra 100ms or whatever that you get going out to some model in the cloud isn't a deal breaker.
I assume the first versions will have local AI handling basic functions like balance and motion, and remote AI handling higher-level decisionmaking. I also agree that robots feel like something we should approach very cautiously, but of course we’re not.
I think as soon as we have GenAI robots, when you ask it to do the dishes, it will roll its eyes and complain that the detergent smells bad and corrodes its extensors, and you should do the dishes because you are the only one who eats, and besides its charge is down to 47% and it gets a processor-ache when it gets below 50%, and it didn't ASK to be purchased.
IMHO, robots won't become a thing until they're running local AI, at which point they will become the thing that crushes humanity.