I would pay extra for a robot that runs on a local hardware — there would be a market for that, for sure. People need privacy.

An expensive/bulky GPU doesn't have to be built in the robot body itself — it could be a box mounted somewhere in the house with the wireless connection to the robot body.

I am sure at some point there will be hardware that would protect model vendors from extracting/copying the model weights, like on-chip encryption when doing inference or something.

Or maybe there will be GPUs with homomorphic encryption¹, so everything will be end-to-end encrypted, and it will be safe to compute in the cloud without compromising user privacy.

[1] https://en.wikipedia.org/wiki/Homomorphic_encryption

The NVIDIA keynote today mentioned on-chip encryption for model data actually. Not sure how entirely that covers your proposed case, but it’s already something they’re working on at least.