Given that emergency personnel were on scene in minutes I suspect that what was lacking was training and a willingness to overcome the reticence to get involved. Handkerchiefs, ties, tee shirts, socks, belts can all be pressed into service to cover the gap as the EMTs are coming your way.

I also doubt that quick-clot, or similar, would have made a huge difference. In the time it took to dig out and open you could have installed an expedient tourniquet or simply applied direct pressure.

IMHO the key is to act quickly. Going with whatever you have on hand, even if it is a partial or incomplete solution, is better than the better solution applied when you get back with your kit.