I agree with everything you said, but I believe the pump shroud is for faster engine warmup, not saving a fraction of a horsepower. Cold engines run rich, producing more hydrocarbon emissions, and the cold startup phase emissions are heavily penalized. There’s also additional wear on the engine due to cold oil and looser tolerances, which affects nearly every aspect of the engine.
It might be, yeah. But why wouldn't the thermostat solve that problem, since it won't let water through the rad? And wouldn't the faster warmup come at the expense of the heater taking longer?
If you really wanted to not run the coolant pump until you'd got the engine a little warmer I would have thought a magnetic clutch like an aircon compressor would have been better. Although these days, maybe even an electric pump could be more efficient.