Most US states don't have an inspection regime. Of those that do, it's often just for emissions (and with 2001+ cars, it's increasingly just confirm the check engine light shows up in the light test and turns off when the engine is started, plus check that the emissions computer says ready for test). The driving public does not want to pay for safety inspections.

But yes, if there was a safety inspection, it should include verifying that lights function and that headlights are aimed appropriately. A brightness test might be too complex, but safety inspection would be the place to do it.

In theory, yes. But, it's state-by-state, enforcement at drive-time is next to zero (unless the cop just wants to hassle you), leaving it to either annual or time-of-sale inspections that are easily gamed (slip the mechanic a $20).

Heck, people will reinstall stock parts for inspection then swap back to the illegal parts. Common with emissions stuff as well.

Only a handful of US states have any type of safety inspection

The only one I've experienced (Massachusetts) wouldn't catch any of what we're discussing in this thread. They put it on the emission testing machine, walked once around the car, maybe checked the brakes, and that was it. It was in no way comparable to the UK's MOT test, which is a proper inspection.

Headlight function (including aim) is on the MA vehicle inspection: https://www.mavehiclecheck.com/motorists-basicinfo

Whether it’s done carefully or not, I doubt, though I did fail one year for headlight lenses too cloudy, requiring a fix and reinspection.

Maine also requires headlight aiming to be checked and compliant.

It's just not done though. There's a list of like 10 items to check, and you are only allowed to charge like $12-$18 for the check, so corners are cut, and your average 18 year old who was given the job of doing the inspection does not care, and enforcement is more concerned with the shops willing to give you a sticker for stuff that is outright criminal, like not really working brakes.