We've had safety inspections in Missouri since the late '60s. It is not a bad thing, really. It is cheap ($12), and while it used to be every year, it more recently went to every other year, and even more recently cars do not require them until they are 10 years old or hit 150k miles.... although the mileage thing has no practical way of enforcement.
We don't have anything for rust hole failure aside from something that would be deemed structural and thus an actual safety hazard. So rusted out rockers and fender lips are not an issue, at least here.
There is no link to emissions testing and safety aside from a visual check, and even that isn't really much of a thing.
Illinois right next to us has no inspections, and in the eastern end of the state, we see plenty of those clapped out death bombs over here. So if there was ever a good reason to have them, we see that every single day.
The problem is, unfortunately, lots of people will absolutely do nothing to their cars unless someone forces them to... and even at that, plenty now just drive around in expired plates or the new thing, expired temp tags. You can only police people so much, and I'm not really sure what can be done about the chronic rule breakers. But I know if you take good care of your car, a safety inspection is a non-issue, and you would/should actually WANT to know if your car has a non-functioning exterior light, or a ball joint that is ready to pop out of its socket, or any one of 100 other things. For 12 bucks, you won't be able to get any other professional in their field to check something out like that. My brother is a plumber, and if you asked him to come check out your house's pipes, it'll cost $85 just to show up.