Well, my situation was a bit different as I was in a special forces unit. For one, we had no women.
>The ultra-badass thing to do was to pre-apply CAT tourniquets (loose) to all 4 limbs, so the operator could then tighten them when hit and continue in the fight.
We've had this practice, but when you have a tourniquet(properly tied, cutting off all flow) on a limb, you have little to no control over it (to test this, tie a tourniquet just above your bicep and try to open and close your hand when it has no pulse). The only thing you can do is use other limbs to make up for the lost one. Furthermore, if that limb is a leg (the thigh in particular), in order to fully cut off the flow, it is necessary to apply so much pressure so as to break the bone (which sucks, but is better than dying). Lastly, even if the situation were dire enough to warrant these measures, where would you place the tourniquet on the limb? This is a problem for a few reasons. For example, I dont know about your unit but in mine, anything on us gets beaten up a lot for various reasons; damage to the tourniquet would be likely and problematic. Furthermore, during an exercise, the amount of blood that flows through your muscles increases thereby expanding the size of the limb. This would cut off blood flow and inhibit performance if you had a loosely tied tourniquet on it. If you resize it to be larger, then it would slip and fall in times of inactivity. Lastly, and this might also be a difference between units, we arent allowed to wear any bright colors, reflective mattes, sharp contracting colores, or have anything on us which identifiably changes our shape so as to mitigate detection. As I said, when it comes to the equipment (especially the medical equipment) everything is boiled down to a science.
>It worked better for immediate response than relying just on direct pressure
This is true, but the problem is the loss of use of the limb. If you are in a situation where you absolutely need to move quickly, a direct pressure solution to slow the bleeding until you are in a relatively safe area where you can then apply a tourniquet is better. A lot of the decisions you have to make are a balancing act of speed versus safety.
>but then utterly hilarious when random people copied them without understanding
This is very true. The number one mistake I see people who havent been trained to use a tourniquet make is they tie it (however poorly) on the injury. You are supposed to tie it 4 fingers above the injury because veins are elastic and when severed they jump back into the body, so you need to account for that and tie it higher.
Sorry if I went on too much, I just really like that so much thought has been put into every decision that we take for granted; if only we knew.