If safety inspections help keep them that why, what is the downside?
That's 'if' is still open. ;-)
Do states like mine without mandatory safety tests really have a significantly higher number accidents?
It's really hard to say due to a large number of other factors like traffic laws, average speed, traffic, etc. that vary state to state.
For example, the state below me, NC doesn't have inspections but mine (VA) does. The number of motorcycle fatalities per capita is higher in NC than VA. Is this due to mandatory safety inspections? Most likely not. Why? Because NC doesn't have a helmet law and VA does.
That said, my gut, personal experience and anecdotal evidence all tell me that safety inspections *do* save lives. I know it's not hard data, so it's not worth much, but there you go.
Look at it from another angle: Why should we have seatbelt laws? If someone is too stupid to buckle up, they deserve to die, right? Here's the thing, seatbelts don't just help you survive a crash, they help prevent them. How? By holding you firmly in place behind the wheel.
Say you're going 60MPH and suddenly see something in the road and swerve to avoid it; without the seatbelt locking and keeping you in place, you'd be pulled to the other side of the car. Now, you're halfway out of your seat, frantically trying to correct the swerve and *BAM* you run off the road plowing through an orphanage full of kittens and puppies.
So, if a seatbelt prevents someone from losing control of their car and hitting me, it's worth it. Same with safety inspections. If it prevents someone from rear ending me because their brakes don't work, or their windshield wipers don't function or they had a blowout, it's worth it.