My main point, however is that the NHTSA report found poorly maintained vehicles are a factor in fairly few crashes. The vast majority of the crash vehicles that did have a maintenance issue had a tire/wheel problem.

Making a guess based on my experience with cars, the problem is probably almost always worn or underinflated tires. That's something a person with 5 minutes of training can check in 5 minutes with tools that cost $10. Perhaps there's better data available, but the report I linked seems to suggest comprehensive vehicle inspections wouldn't have much more impact on crashes than quick tire checks.