Oh, if you drive it "right" it's generally safer to drive it fast at a drag strip than it is on the street. It's a controlled environment with optimal conditions, generally. Sometimes accidents happen. IE, the 70 Chevelle that went down the lane before you dropped some oil and he did the thing they always do and don't tell the safety guys that he popped an oil leak. So, when you go, maybe your tire hits his oil patch and it gets a little slippery.
In the above example, if you have it in sport traction, the car may depart a little sideways, but the traction control should step in to reduce power. If you lift off the gas, it should snap back straight near instantly. The people that have issues will be running in track settings (because they think it's cool to be in track at the strip... when that setting is for road track use). They lose traction and go a little sideways, fail to lift and now have to drive it out of a drift at 110mph. A competent driver can pull it off, but I don't know any "good" drivers who would ever be in that setting in the first place. This is the type of situation that often ends with the car pulling right, then left, then more right, then more left until their door smacks the wall.
And, when I see this happen, what I also hear is the constant roar of the engine. Idiots like this tend to stay in the gas too because, "lifting is for pussies!" That's how that "death wobble" gets wider, and wider, and wider as they just keep adding more momentum. Eventually they run out of road.
It can all be usually fixed with taking one's foot off the gas.