I've had some lightly cooked oil very soon after putting power steering on. Before I got one installed. Always run one.
Never ran a huge one. Even Ford did some very primitive coolers, long piece of hard line either bent into loops or serpentine. The factory Bronco coolers were right on the pump getting hot air after the radiator. My newer ¾ton van has a very simple tube and fin cooler. It doesn't take much, but you really should have something.