One more thing I just thought of; if it's a 3-wire dryer circuit, he can't
move it to a subpanel and be kosher. It would have to be 4 wires if fed
from a subpanel.

And that is because it is illegal to create a 3-wire dryer circuit and the
old one is grandfathered, or is it something to do with the subpanel itself?

If it the new circuit, he could move the waterpump. The ones I have seen
don't have neutrals.