Yes a pump installer is required by the NEC to add a grounding wire to an existing installation if the pump is pulled and reinstalled.
This has been the law for over 30 years. Agree or disagree with the NEC, it’s still required.
Fortunately my well people did not see it that way when they removed my pit and reinstalled the pump with a pitless. Maybe codes differ. Maybe interpretations differ.
The wires from the house to the well are buried. I wouldn't have liked them to having to install new wire with a ground to the well.
Actually, there were 3 conductors run underground, because an earlier pump had been a 3 wire. But a ground wire needs to be bare or green. To re-purpose a red as a ground would not be allowed under the NEC I think (NEC 250.119). So my red is taped off in case I want a 3 wire pump some day.
I think it is permissible to replace an existing electric oven or stove where the neutral wire is connected to the frame. Running new wire is not required for that. Now that sounds a little dangerous. Not having a ground wire to a submersible pump seems really safe to me.