Why would consumers settle for that? Local models have scaled quite quickly. Just pair the bot with a LAN server as the brain that keeps all your data private.
Barring that, choose bots that use Zero Knowledge Proof architectures for all data so you know there's no in/out of personal data, only security proofs. This makes rental robots certifiably private too.
They've settled for that in:
* Phones * Cars * Robotic Vacuums * Kitchen Appliances * Televisions * Home Lighting * Home security systems, doorbells, and locks * Web browsers * Operating Systems
So, uh, yeah, I'm pretty confident users will settle for that in robots too.