It's a bit similar in Germany and the EU. Cars, which doesn't pass the regulations about safety or environment, cannot get a registration.
It depends on the date of registration and the regulation, which were valid in Germany or the EU at that time, with the exception of the lighting. The rules for the lightning (clear non-sealed-beam-headlights, red taillights, turn signals, hazard-signal) go for all vehicles, also antiques.

The difference is, that cars, which fail hasn't neccessarily to be destroyed. You just cannot it use on public roads.
Sometimes you may get a special permission for a single registration, but this depends on the local TÜV and the local traffic authority. You cannot generalize that.

So all Citroen Mehari with a German registration do have such a single permission. This model never got an official general ABE (https://de.wikipedia.org/wiki/Betriebserlaubnis) due the inflammable body

Same with the Chinese Brilliance BS4, due the failed crash tests.

It's also impossible the get a registration for a South African Citi Golf or a late Brazilian made VW T2.

When the problem is not a missing catalysator or a failed crash test, but only the lighting, you may can get a single permission, when there is no chance to get EU-law-conform parts, for example no orange back indicators for an US-spec model, which was never sold here.
When there were EU-spec parts, no never get this special permission, for example for a re-imported newer Porsche.

No exceptions are possible with taillights. An acquaintance has brought an Australian Ford Falcon to Germany, a car, which was only built as RHD.
As there was no possibility to get headlights for right traffic, he had to bring the car back to England, where he has bought it.