I assume the rolled eyes are intended to indicate sarcasm, but I'll approach the tailhook issues anyway.
Installing an arresting cable similar to the ones used at Air Stations and aboard aircraft carriers seems, on the surface, like a great idea. The idea being, I suspect, that in addition to NHRA controlling chutes, fuel and ignition, they could also lower an arresting hook at the back of the race car to catch an arresting cable stretched across the track. The problem is the height above the ground that the cable must be in order to be effective.
Air Stations use rubber donuts, spaced evenly across the ruunway to suspend the cable high enough for the arresting hook to catch it, then arresting gear engines pay out cable at a rate that slows the aircraft to a stop in about 1,000 feet.
Aircraft carriers uses metal arches, connected to the flight deck, that are spaced evenly to hold the cable up and again, arresting gear engine pay out cable to stop the aircraft in an even shorter distance - from about 145 kts to zero in about 800 feet.
The primary concern, as I see it, is the cable being two and a half to three inches off the ground - it would tear up most race cars that don't have that kind of clearance. No big deal for the cars that are using it to stop themselves, but for cars that are able to stop without the arresting gear - not good.
I'm not saying it can't be done - anything is possible. But it would be very expensive to maintain and would require a lot of modifications prior to use. All of which is worthwhile if it ends up saving lives.