Yes, they should, but there are a couple of things to consider here. In most countries we are talking about very low numbers of cars that are exempted. You can see this as a safety valve of sorts: provide some leeway to ensure you don't give the automotive lobby reason to push back too hard against regulation. Because the automotive lobby is insanely powerful and you need them on your side in order to ratchet up regulations. (And I'm not just talking about those that represent the industry).

What you really care about is that we are able to tighten regulations for 99.9% of cars. That's what is going to make a difference. Not running after the 0.1%. It just isn't worth the effort.

And we do this for new cars. We constantly ratchet up the safety requirements. Ensuring we slowly make the overall fleet safer. Not only do the Euro NCAP rules get stricter over time (hence "ratchet"), but the "NCAP star rating" is being tilted towards what are now termed as "Vulnerable Road Users". (Note that the percentage weights haven't changed that much but the rules that decide the number of stars have).

(The reason we now have the concept of Vulnerable Road Users rather than just pedestrians is so we can broaden the scope to include cyclists)

Note that the 99.9% / 0.1% figures are _guesses_ and that they are most likely way too conservative. I was not able to find exact official figures on exactly how many excempted cars are have valid registration. But I could find some numbers on the specific class that large US pickup trucks belong to. And when you compare these to total automobile sales, these numbers are trivial. That's 0.076% of EU car sales that year, and 0.057% of European car sales.

It would be thoroughly pointless to focus on them.