Well, maybe not--even though the water pump is turning all the time, the load imposed on it by pumping through the radiator is probably greater than if only just the coolant in the engine. In other words, with the T-stat open the pump has a significantly greater mass of coolant to move, over a greater distance and in a draggier pathway.

I agree that cooler underhood temps are better for most things that reside there, especially rubber or plastic.

Just be sure your wrap material does not contain any chlorides. I've seen plenty of insulated stainless tubing destroyed by improper insulation.

yeah actually road salt will make a mess of SS, so if a vehicle is winter driven, you can't be complacent about SS under wrap.

wrong about pumping resistance. when the thermostat is closed, the pump has to get x volume through the bypass hose. when the thermostat is open, the pump has to get x volume through the bypass hose AND radiator. more/larger path with the same volume=less pressure/load

If you are worried about heat from the exhaust, try getting it coated. Something like, high heat ceramic coating. https://www.hpcoatings.com/default.aspx I have no experience with this link- just used it as a reference for those who did not know what I was talking about.