That’s the point of the question. Is this the result of convergent evolution or are Boston Dynamics simply mimicking nature’s solution? Even worse, what if the bird-like head motion has no functional value for the posed problem?

imho the motion looks entirely like a simple counter-balancing solution to keep the robot upright and the box steady. It does look like a whole-body solution, not a per-joint PID. Others have mentioned they use MPC which makes a lot of sense here. I think it's just "convergent evolution" if you want to put it that way.