Aisha Harris looked at the past, present, and future of pop-up headlights:

• Pop-up headlights have been around since 1936 when the Cord 810 Convertible first featured them.
• They’re sold for their aerodynamic advantage, although the effect is extremely small.
• More likely they appeal to our predisposition towards anthropomorphism as they take the most human looking feature of the car – the eye like headlights – and add eyelids to them.
• The last real car to feature them came out in 2004 (pictured above).
• They seem to have been a victim of EU Regulations which require the front of cars to be more readily deformable for the sake of safety.
• While it’s possible to design pop-up headlamps around those requirements it’s expensive and not worth the cost.
• The regulations may only apply in the EU but since car manufacturers work globally those requirements have affected their designs around the world.
• Headlight innovation isn’t dead yet. Adaptive headlights are being developed that adjust light beams based on how the driver is driving.

See some photos of pop-up headlights through the ages, the American regulatory framework for headlamps, and why they were most popular on sports cars in the 1970s over here.

Source: Slate