Also: since the listings on the marketplaces for these lamps do not match legal requirements, why are they not shut down and the sellers prosecuted?
In New York, where I live, inspections are done by private mechanics (with a state license). There's a posted inspection standard (https://dmv.ny.gov/brochure/new-york-state-vehicle-safetyemi...). Lights must be "of an approved type," but I'm not sure how you can reliably check this in a shop.
Also, some mechanics are more stringent than others. Some are outright shady. New York sets a flat $37 fee for inspections, paid to the mechanic. The fee is low, so there's an awful incentive here to look for high-margin items that "need" to be repaired to pass the inspection. Brakes and windshield wipers are some of those items. A set of aftermarket light fixtures -- if they can even be identified -- not so much. (This is anecdotal, but I've experienced this type of inspection on more than one occasion.)
Other states, like New Jersey, do inspections solely at state-owned inspection facilities.
Regarding sales, it's not illegal to manufacture off-spec fixtures. It's illegal to have them on your car on a public road.
Even for a 20 year old car, you will be told stuff like "you need to replace the front left wheel bearing and the tie rod bushing, both rear springs, and that ABS sensor which is not working". You'll even get a fail if you show up without wiper fluid (since then they can't verify that your wipers are working correctly). They most definitely check your lights thoroughly.
Around here, just having the test done is almost $100. Then there is the (potential) garage bill or DIY work+parts to fix whatever didn't pass, and then $20 for the re-test to fix whatever was necessary. If you don't do it, you lose your plates and insurance coverage.
But usually the people who run aftermarket lights take the required 1 hour to put the stock ones back in before the test.
I once got a car checked out, and the mechanics noticed that one of the brake cylinders couldn't be bled when they replaced the fluids. When I got it back, there was almost no brake pressure and the report had a note lightly recommending that I get the cylinder replaced at my convenience.
You would be amazed at how averse people are to maintaining their cars in the States. Even the dealerships will avoid telling you about problems because they assume most people would prefer to run things into the ground rather than maintain them. It's pervasive.
I assume there are not enough law enforcement resources to enforce all the relevant laws.
Varies by state.