Do car safety inspections have any impact on road safety?

We've received MANY questions over the years about car inspections here:

• Why does Vermont have a vehicle inspection requirement?
• Why are those requirements so strict?
• Do they make Vermont roads safer?
• Who's in charge of the rules?

Are you a car mechanic or someone with expertise in this area? What have you heard? Who should we talk to/where should we go to answer these questions?