Not playing defense for the guy not having a cage here..
When you are on the street, you are driving around without a helmet, likely not using the 5/6pt harness to keep you in the seat. In an accident is your unprotected head and body move about the cabin and hit VERY hard objects like the cage, usually causing head trauma and other broken bones that wouldn't otherwise be found in a stock car at legal speeds. The head trauma is the most dangerous part of it.
If you have a cage, you should always be wearing the full harness, even if you decide to go without the helmet, it will keep you strapped in place if something happens.
If I was at an event with a car that serious I'd probably have a full cage + hybrid HANS setup.