I was fortunate that my EMT training, provided by my employer (National Park Service) emphasized wild situations and inability to reach a medical facility, which standard Red Cross (call 911) certainly does not. Most of my experience over the last forty years, both on the job and as a volunteer, has been in fairly wild, off road settings. Most of my experience came when tourniquets were out of favor, and considered only a last resort. I have been a first responder at probably about two hundred incidents involving bleeding. In all cases, a firm bandage and dressing, augmented occasionally by direct pressure, stopped the bleeding.

One of these was a virtual arm amputation (subject walked into a rear helicopter rotor) but apparently muscle spasm clamped down the blood vessels.There was surprisingly little blood involved. Good thing - where do you apply a T when the arm is off at the shoulder?

The cornerstone of my first aid treatment is an elastic bandage,used for immobilization of a dinged appendage or, properly applied, as a pressure dressing on a bleeding wound. They are not the kind of thing you apply and forget. Watch them carefully and readjust as necessary. It is best if the patient is conscious.

In any case, your equipment should reflect your training and experience. This discussion is a splendid example of this....