Older cars and lack of maintenance can easily be an issue. That's why I assume rudimentary safety inspection is a must. Part of an overall "tighter regulation" package.
(Cough cough) While I acknowledge I drive a 29-year-old car, I speak with complete disinterest when I say I can't really support measures that burden those who try to help the environment by keeping their current vehicles running.
The NHTSA actually did a study.
In the year 2015, 94% of accidents were caused by driver error, and 2% each by vehicle failures, environment, and “other”. Of the 2%, 35% were tires, 22% were brakes, 3% were steering/supension/transmission/engine, and 40% was “other”, sue to incomplete police reports. Even if we attribute all of the “other” to either tires or brakes, which is all they check in state inspections really, then that works out to about 40K of the over 2M accidents.
The next step would be to look for a statistically significant difference between inspection jurisdictions and non-inspection jurisdictions. One would think there would be one, but I really doubt it, considering the very cursory inspection most states perform.