I've worked in LE, security & served in the US armed forces.
I'd think it's smart to have a small "blow out" kit or a few medic/first responder items if you are packing heat.
Quik-Clot is popular. I've seen a few pocket size 1 person kits here: www.galls.com www.uscav.com www.natchezss.com www.policehq.com
Kits may help you render aid to a victim or protect yourself after a serious injury.
NOTE: I honestly wouldn't provide first aid to downed or wounded subject after a use of force incident. I'd contact 911/EMTs/fire-rescue & let them treat the injuries. I'm not a medical doctor & I'm not a sworn LE officer. I'm also 100% sure that after a shooting event, many "lie"-witnesses will claim you were hurting or torturing a harmless victim. As a security officer, I've seen events spin out of control by bystanders & "witnesses" who were pushing a agenda.
Consider too that a wounded subject could also be a threat or attack you.
Former US Surgeon General Richard Corena(check spelling), US Army combat veteran, medical doctor and sworn LE/SWAT officer had a documented incident where he was required to kill an attacker. The subject was in a motor vehicle accident & attacked Dr Corena as he ran to the scene to provide aid.