There are some perfectly reasonable arguments against the cost-effectiveness of mandatory vehicle inspection, but I have some doubts about the validity of those arguments. Road safety and traffic law enforcement involve a lot of complex interrelated factors; Creating a culture of road safety is difficult to distil into discrete interventions.
There's a libertarian argument that driving a car with bald tires is a matter of individual liberty, but obviously that's a vastly broader argument than the question of mandatory inspection. If you're going to have laws against driving a car with bald tires, it's less onerous and more effective to primarily enforce those laws through administrative rather than criminal justice mechanisms.
https://en.wikipedia.org/wiki/List_of_countries_by_traffic-r...
As is typical with US regulation, it's a "worst of all worlds" hodgepodge that makes no logical sense.
Over here, we can freely import pretty much anything. If it's more than 10 years old, you just register it. If it's less than 10 years old, you can still bring it in as a personal import, but it'll need to pass a slightly enhanced version of the normal annual inspection. It's a point of principle that any vehicle that passes inspection should be road legal, hence oddities like this:
https://www.youtube.com/watch?v=paIGBOlkQr0
Because we're a right-hand-drive country, Japanese imports are commonplace. If you want a Kei car or a JDM-only luxury minivan, you can just have one. That taken-for-granted freedom gives me a certain degree of empathy for the 2nd amendment lobby.