That's why I have an Israeli bandage in both of my cars and am procuring military style tourniquets, plus other stuff for a roadway trauma kit. One is already in my wife's car, and I'll nab another one or two the next time we open up some "expired" ones during training. Quikclot is next after that if I can find a cheap source of the quikclot gauze. Not fond of the quikclot sponges but the gauze is very expensive.
Uncontrolled bleeding in an extremity is a very common yet often completely preventable cause of death. A properly applied shoelace or belt and a tiny bit of training can easily make the difference between life or death. I'm a total slacker for not having completed it yet, but my goal is to have a decent trauma kit in both of my cars that is suitable for caring for up to 4 people. 4 of everything, including compression bandages, tourniquets, quikclot, nasal pharyngeal airway tubes and surgilube, in addition the other usual first aid items like those moldable flexible splints. I'll probably even include some of that liquid skin glue since it can be used to close up nasty glass cuts if there is any delay expected in receiving professional medical care. I priced it out since nobody except some extreme survivalist stores sell complete kits, and I expect each kit to cost over $500 unless I can find some of the military grade stuff at a surplus sale. Just a single quikclot gauze package is upwards of $30, and the really good battlefield tourniquets you can apply with one hand are about the same. Quikclot sponges are a lot cheaper but I haven't seen them in use and wouldn't want to count on them without seeing them in use.
The last time I was the first to arrive at a car accident, all I had with me was a hand towel. Luckily the crash victim was asleep and completely relaxed during the accident (she fell asleep driving and drove off the road) so her only injuries were minor but messy hand, forearm, and facial cuts from broken glass. If it had been worse, I'd have had nothing but jumper cables, some elastic cargo tie-downs, and my clothing available for improvised first aid supplies.