This is a bit of a dicey subject to a friend I have in the insurance industry. Purpose built race cars can get insurance but not the type you think. And it's an expensive proposition. However most I know that track expensive cars can basically call the dealer as they crawl out of the wreckage. So it's self-insurance. One more item, and we are all far too fine a collection of gentlemen to consider this; but I've heard of some unsavory types getting some insurance money on track damage claiming it occurred on the road. While they were inside delivering toys to the needy, no doubt.
Interestingly, insurance on PWC, quads and snowmobiles is easy to get, easy to claim and very inexpensive. Yet most, if not all, of my seat time in those conveyances involves activities that would be considered, at best, "tracking" at worst hooliganism. Yet Progressive let's you get ORV insurance after a few questions online. Not that I would use that particular company.
In the interest of full disclosure, I've wrecked a few of the above whilst in sport mode, if you get my drift. I just make sure to heat gun off the number plate.
Arctic Cat, makes a sled that is indistinguishable from what a pro races, including sponsor stickers. You can insure it for under $1500. Imagine if you have a car in full race livery and you bring it (or tow it) to an adjuster?
I realize full well that you can't compare a $20k ORV to a $300k car in terms of cost to replace. But there is a blind spot there when talking about track days in road cars.
But as was said, a personal liability umbrella policy is mandatory when you have flashy toys. Deep pockets and all that. Lawyers salivate at the thought of Ma and Pa kettle getting into a traffic accident with a prick driving a supercar. IMHO, of course.