According to Wikipedia, many US states have a relaxed policy for car inspection regulations:
Maryland requires an inspection prior to registration or transfer of ownership only. Several states have abolished their safety inspection programs in recent years, claiming that these programs do not reduce accidents and are merely a tax on vehicle owners.
Some states, including Florida, Kentucky and Minnesota, have discontinued their testing programs in recent years with approval from the federal government
The same article mentions various regulations throughout the world and most of them are more or less "car inspection is mandatory every 2 years after a certain vehicle age".
According to this article mandatory inspections might help with lowering accidents:
The observed probability of accident involvement (as measured by either rate) was found to increase with time since last inspection. This result supports the alternative hypothesis that a mandatory safety inspection has an immediate safety benefit which decreases over time.
[EDIT] Since comments correctly point out that car inspections might lead to less air pollution, I am also including a reference to sustain this. This article argues that emissions checks might lead to reduce of air pollution with certain substances:
Using over a decade of data from the state of California, we show an increase in emissions-related repairs, as proxied by passing post-repair inspections, corresponds to local improvement in CO, NOx and PM10 levels, but with little change in local O3.
However, additional gains from the Smog Check program are decreasing with time, as almost all benefits of repairs and re-inspections come from fixing failing older model cars (1985 and prior) with inferior emissions control technology. As older technology cars disappear from the road, the differential between failing and repaired emissions decreases.
Question: Why do so many US States have a relaxed (or none at all in some cases) vehicle inspection policy? This seems to be quite unusual when referenced to other countries and also seems to be less safe.