> I am unaware of any barrier, or any reason to infer there is one, for dextrous robots.

I don't think there's a fundamental barrier to building a humanoid robot but the cost will be an extremely high barrier to adoption.

A human is nature's ultimate robot: hundreds of servos, millions of sensors, self-assembling from a bag of rice, self-repairing for minor damage. You just can't beat that, not for a very long time.