How exactly would you even fail the safety inspection besides something obvious like not having all your lugnuts on or flames coming out from under the hood?
Thin brake pads, obvious fluid leaks, brake light out, bad wheel bearing, cracked windshield, loose battery, obviously old brake fluid, dried out radiator hose, non-compliant helmet, etc, etc - all can get you sent packing. Reaching speeds of up to 140mph is serious driving - if a car has a weakness, the race track is not the place to find out whether it's serious or not. The stresses the track will put on your car will likely magnify any issue it has now. Inspections are meant as much for the other participants' safety as it is for yours. You'll be at the limit of your skills and your car's abilities, with others depending on you and your car to be predictable and reliable.

You want to make sure you've done everything you can to prevent these sorts of incidents, since you're relying on the same courtesy from the other participants. You have to realize that your mechanical failure can lead to not only your embrace of the armco or tire wall, but to others impacting the wall backwards at speed and ending up with a portion of your car being delivered to you in a bucket. If you dump fluids, someone else may be following close behind and get caught up in your incident.
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There's another aspect to it, regarding ensuring your experience will be a good one. If you fail the inspection, there's no refund. If you have mechanical issues during the event and can't get out for your assigned session, there is no refund. This isn't meant to scare anyone away from coming out, but it is meant to underscore the importance of making sure your car will pass the track inspection without a problem. You'll have a much more enjoyable time if you're sure your car is in as good mechanical shape as possible. It's way more fun to be out on track than to be running around trying to beg tools or find spare parts in town.

Track days are amazing - they can almost be life-changing in the amount of thrill they give you. But it's important for everyone who participates to take their own safety and the safety of others seriously. Don't skimp on the inspection check list. Make sure all of the items listed are performed as specified, and you'll go a long way towards making your "luck" work in your favor at the track.