You so funny, you must be on city council.
The 'punch holes in targets' is a derivative use, using targets instead of people. To kill game is a pathetic attempt; tell me, who hunts deer or ducks with a handgun in North America?
The third is stupid - the whole point is to kill people, and you hope the intruder runs away first. That's the whole point of a handgun, if it wasn't meant to kill people, you wouldn't carry it for self defense, you'd carry a banana. The whole point of a handgun is that it is for killing people, and you hope people are scared off by it. That's the point of it.
First, you punch holes in paper to become proficient with the firearm for the same reason I have to go to sim every six months to be proficient in what I do. You hope to never have to kill someone just as I hope to never have to deal with the catastophic failures simulated in the sim. But when you do have to meet the challenge, you are able to react decicively because of training and repetition rather than by guesswork or instinct.
Second, yes, handguns are used for hunting. I have used my .22 Ruger to hunt grouse. I have fired a Thompson Centre Contender that was chambered in .257 Roberts, ideal for deer and I can hit a 4" steel target a 100 yards, and buddy also has a .410 shot barrel and a .410 slug barrel for it. I want one in 300 Savage, (because I already have the dies for reloading them). They are only illegal for hunting in Canada because our wimpy Canadian masters have an irrational fear of hanguns. Hunting pistols are as accurate and powerful as rifles. I was not convinced until we tested both with chronometers and other high tech gear. The only advantages a rifle has over a pistol are that they give a more stable shooting platform while standing and the weight helps to absorb the recoil. The barrel length of a rifle is actually a detriment to accuracy because it flexes, the longer the barrel, the more the flex, or whip.
Third, yes, all basic firearm designs come from the need to kill, though they can be modified for different purposes, but the basic design is the same. A handgun is designed as a defense firearm, it is a reactive tool. If you go looking for action, take some friends, and a tank. A pistol allows you to fight your way back to your gun. It also allows you to get yourself out of a threatening situation, a banana won't do that. Sure you hope you'll scare away the assailant, but you have the access to force if you need it. At my age, I know I can't outrun or fight my way out of a situation. Defense of self and those under my care is a basic human right and that far and away trumps anyone else's right to the "feeling" of safety.