Well, linear things translate trivially to relative motion, but quadratic things do not, and also energy is supposed to be conserved, so the natural conclusion is ???!?!?!

That it actually works out mathematically is not so trivial that most people can just eyeball it; hence, it's worth talking about and showing that, actually, it does work out. (As the OP did with the force-against-distance graph, illustrating that it's consistent both ways.)