Brilliant deduction. Now, explain to me. How often do you see a map where all the huntable animals are dead? How long do they stay empty? What happens when one random jackrabbit appears and your entire fort population rushes across the entire map to kill it? What if the player actually wants real hunters instead of having Joe Armourer and Jill Clothesmaker killing everything, but still wants Joe Armourer and Jill Clothesmaker wearing something that won't let them get incinerated by fire imps?
Even putting aside all that, you'd have to first actually hunt the map to exinction, something in all my years of playing Dwarf Fortress, I've never personally seen happen in a permanent fashion. Even if you did so, you'd have to contend with everyone who's wearing armour not doing anything but hunting (since it has such a high task priority) for the entire duration of the extinction process, which, regardless of "doesn't take nearly as long" is still a bloody long time considering animal respawn rates. Not to mention the fact that you can't organize or control your hunters as you could military dwarves, during that entire period, you've got mangy, uncontrollable, morons running all over the map in a non-unified, easy-to-ambush-and-kill-fashion chasing game.
While I understand you are providing a solution to the armour-wearing problem as best as you can; I don't understand why you are attempting to counteract this simple suggestion of merely allowing civilians to wear armour with something that merely causes more headaches. It's like trying to get a baby to drink out of a tiger's teat when you've got a bottle of milk in your hands.