There are certainly cases where harmonic distortion is a problem for a device. It’s just that everyone is left guessing, and there’s an overblown fear of devices being harmed.
Sure. It’s just rarely what lay people associate with “sensitive”. Most customers are worried about small electronics with switching mode power supplies that wouldn’t have a problem with just about any power source.
I wouldn’t run some AC motors, old AC clock, ham radio, or many other things on some generators.
The line is open to interoperation and never defined by the manufacturer. It’s blanket liability avoidance that confuses customers.