The Longbow radar weren't around when they designed the AH-1 and retro fitting it would require a major redesign of the rotor assembly.
They didn't see a need for it.
The longbow is great for stopping the Red Horde(c), less so when fighting fourth and fifth rate militaries and insurgents. Guess what the US has been fighting since 1950.
You're totally ignoring the fact that you can do GMTI and SAR mapping with Longbow which is useful no no matter what sort of conflict you're in, considering that I would replace the rotor assembly with new blades re-designing the rotor-head to accommodate a radome wouldn't be out of the ream of sensibility would it?