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Bruce Cartwright
Respectfully, the amount of people who are not long term medical professionals or instructors that I've seen with the ability to construct a functional improvised tourniquet numbers zero, and the efficacy of improvised tourniquets even among professional providers is mediocre. Improvised tourniquets had a ~2/3rd failure rate in OIF/OEF when studied, and that was when improvised tourniquets were still a widely taught a practiced intervention in the military when purpose built tourniquets were only beginning to enter service.
And even if I can make a properly functional improvised tourniquet using a cravat/bandana, the chances of me doing it to myself are extremely low, and virtually impossible if I'm shot in an upper extremity. Extremity hits are common in shootings, particularly in gunfights to the upper extremities.
Besides improvised TQs, cravats are useful for bandaging a non-life threatening wound on smaller limbs but their short length and lack of compression very quickly limits their usefulness on junctional bandaging, larger limbs, and larger or more serious wounds.
While appealing to nostalgia and the classic American sense of ruggedness and self-reliance, my professional opinion is that this is a bad idea if you're actually trying to prepare for medical contingencies contextual to the carriage of firearms.
Cravats are indeed very useful and a part of my kits, but the last 2 decades of trauma care has pretty well dismissed the idea that all one needs is some cravats and American ingenuity.