I mean its actually very common that cops carry a tourniquet on themselves that sometimes also contains simple first aid. They have duty belt and ballistic armor carriers for them and everything.
Also if you really want to base your rationalization on reality and not gameplay balance, if altis existed as it does in our servers all cops from everywhere would be much more heavily armed, armored, and there would only be lethals...No one is trying to taze a madman with a rifle and body armor, let alone one with a sui vest or a rpg.
So basing it more on balance, it makes sense. Not the biggest bag ever, but one big enough that you can carry a decent kit with you. It still is nothing compared to the csats, 7.62s and large bags rebels get.