You implement mild inspection laws and they do nothing because people can just pay the fine or whatever.

You implement invasive inspections where people are rich and they do nothing because rich people already don't drive on bald tires and whatnot.

You implement invasive inspections where people are poor and you create incentives to circumvent the law and hardship among those who don't ignore the law.

Mechanical failure is a negligible cause of accidents and injury so applying lots of effort co chase something that's only a source of the minority of problems is kind of a fools errand to throw a ton of societal resources at it.

If inspections really make the roads safer it would be an insurance thing and you'd see differences in premiums that reflect differences in law, insurers setting up their own programs where none exist and lobbying states for inspection programs. You basically never even hear a peep out of them about safety inspections unless it's in the context of getting people to upgrade to a newer car with better safety tech. Contrast with intoxication, distraction and driver training which are issues that insurers and their lobbyists constantly weigh in on.