I'm a prior-service US Marine (got out in 2011) and one of the things that bothers me about the current bleeding system is that a simple bandage or rag wouldn't be enough to stem the bloodflow from a arterial wound, particularly in your arms and legs.
I suppose this would be dependent upon having separate hitboxes for your limbs.
You get shot/stabbed in the arm or leg. There is a RNG check to see if it is arterial or not. If not, you bleed like normal and heal like normal (bandage/rag + healing status). If the hit is arterial, you start bleeding massively. You apply pressure using a rag or bandage, but it isn't enough to stop the bloodflow, so you apply a tourniquet.
This would provide some interesting gameplay elements. Suppose you get shot in the arm. Currently, your aim gets thrown off and you have increased sway. While a nice compromise, the real issue here is that if you got shot in the arm you may not be able to physically lift your weapon, much less be able to sustain the recoil and get proper sight picture/sight alignment.
On top of that, if you leave the tourniquet on for too long, you could possibly risk having the limb not be viable again - getting gangrene or having flesh rot would be an interesting mechanic. Suppose you have a higher risk of getting an infection (non-Z) and would require antibiotics and resulting in reduced stamina and getting the chills.
Ways to prevent infection would include closing the wound using alcohol/disinfectant spray cleaned needle and thread and clean rags/bandage. By using both, you can remove the tourniquet.
Ideas for items that can act as a tourniquet:
-Rope -Belts (civilian, police, and military - can attach pouches/holsters/canteen/medkits to them as well) -Actual mil-style tourniquets (CAT, clothing with built-in tourniquets ala Blackhawk I.T.S. - see www.youtube.com/watch?v=4mpcGvs5Pvo )