From a personal point of views, if someone’s seriously injured, which it appears you were, the clothes are cut off and left on the floor where I’ve dumped them. If you’ve got a bag with you, that will come in the Ambulance to Hospital with us, failing that it’s up to your mates or the Police to collect your kit and do something with it.
Frankly I’m not bothered about kit that I’ve cut off patients as there’s usually a slightly more pressing thing to be dealing with like their general health and wellbeing!