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On a sunny day, a car hood can get up close to maximum coolant temperature just parked, so there would not be much left for cooling. A belly pan, OTOH, is safer and cooler but more prone to damage. AFAIR, the 1911 Napier Railton was the first and last surface-rad car, with copper tubes surrounding the engine and leaving only top access for quick service.
Theoretically, one could run a big duct through the car to raise pressure at the back, but the overall effect is to make the car bigger for the same useful volume, with more surface area.
The air pressure at the base of the windshield is generally lower than at the front grille. Leaving it alone is not a waste, unless you use a fan to grab low-pressure air for ventilation elsewhere. There might be a small gain to letting air flow slowly through the interior, since even a rough duct has little drag at low speed.
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