A contrary opinion here. I have attended many scenes in outdoor settings, using my EMT training to good advantage. Direct pressure, usually involving one or two gauze pads, worked to stop bleeding. Occasionally we had to resort to IV technology in case of severe blood loss.

One of these situations involved a bystander who walked into the spinning rear rotor of a helicopter, virtually severing his arm near his shoulder.

In any case, you need a balanced first aid kit ready for lots of different situations, so make room for other items.

While sterility is highly desirable and a worthy goal, it is difficult to maintain in an accident setting. If you must, resort to non-sterile items. the goal is to stop the bleeding.