Why should that be required? Let people do as they will and impose penalties for problematic behavior (including negligence). I lived in a state with safety inspections and AFAICT it was little more than yet another disproportionate speed bump for the poor and a complete waste of time for society at large.
I do see the merit of inspecting larger trailers (such as for boats) once a year given the combined increased likelihood of incompetence and risk to life when things go wrong. But even then I think it doesn't actually accomplish much in practice. The time and effort would be better spent on targeted public education campaigns, possibly mandatory.
For emissions, again who cares. Regulations imposed on the high volume manufacturers broadly solves all the issues that are easy to solve. The rest are either willful violations or collectors. The latter is technological in nature and inevitably gets grandfathered for both safety and emissions everywhere I've lived.
For emissions there is often nothing visually wrong with the car. So you’d essentially be giving up on enforcement if you didn’t require everyone to get their car checked at least every few years. Doing it every year is IMO overkill.
As to safety inspections it’s not a very large effect, but they do save lives and the expense is generally rather small. Yes it impacts the poor more, but that’s because getting unsafe vehicles fixed or off the road is kind of the point.
I live in a country with mandatory (mostly-)yearly car inspections (and all other motor vehicles).
Many time you don't even know that there's an issue and they only find it during the inspection. Handbrake works only on one side, normal brakes don't work properly on one of the wheels, there's play in one of the joints or tie rods, etc.
You park, pull the handbrake, you have no idea that if you parked on an incline, your car would roll downhill, but because they noticed it during an inspection, you get that fixed. At the same time, you're forced to replace all the blown lightbulbs etc., even the ones not used daily (fog lights, etc.), since they check those too. Many people don't even notice their brake lights not working.
I’d disagree. It keeps cars with bald tires, faulty brakes and other defects off the road. Poor people who can’t afford these things shouldn’t be driving the cars.
Motor carriers have a totally different regulatory regime that has a direct influence on highway safety. The issues there are due to the varying jurisdictions.