Meta-analyses show that studies vary between not being able to find a firm conclusion, or pointing to the conclusion that safety inspections make roads safer: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8296297/

Much of Europe has much more stringent vehicle inspections than even Mass, (Germany as the most notable example). The most English-friendly single-case study I found was out of Norway, and concludes firmly that inspections reduced the number of unsafe cars on the road, but resulting accidents and fatalities were not reduced by as much as expected, and posits that drivers of cars with faults that would fail inspection know that and adapt around it, to an extent, or are so negligent that they will crash no matter what the condition of their car. (https://pubmed.ncbi.nlm.nih.gov/16887091/).

On a more social-contract style argument, many if not all of the things tested for in vehicle safety inspections are directly related to how safe and easy it is to share the road with others in different ways. Front plates make it easier to have accountability for tolls and thefts. Better emissions benefit us all and all of our offspring. Proper lighting make it so I can see your car, and that you aren’t blinding me. Effective brakes and tires mean that you have more power to evade or mitigate a crash whether it’s your fault or not.

Interestingly, the meta-analysis also concluded that all these things that inspections make sure are in “working order” are just givens for newer cars- your 1990 Honda Civic in perfect condition is still horrible compared to a 2016 Honda in okay shape, and the 2016 also doesn’t have nearly as much time to wear out. Because of this, they say it may make sense to cut out all of the cost for the government of running these inspection centers and instead pump that into subsidies to allow people to buy newer, safer cars. (But most dedicated scientists, scholars and enthusiasts in the automobile world will tell you that the last time we tried to subsidize new car sales and get old cars off the road, Cash for Clunkers, was a disaster and had horrible effects on both the enthusiast and general used car market).