Most of the hunters I know use bolt action rifles, including myself. However, that’s not to say that I don’t know any that use semi-auto. My uncle uses a Remington 7400, for instance, and one of my coworkers turkey hunts with a Mossberg 930 semi-auto shotgun. Speaking from experience, a quick follow-up shot can make the difference in a hunt because, contrary to popular belief, the animal doesn’t always run after you miss the first shot. For deer, you’ve got about a 50/50 chance that they’ll freeze up for a few seconds in surprise, then they’ll take off to the nearest clump of cover. If that cover is only a few meters away, you can get a second shot in with whatever rifle most of the time. If it’s farther away, you’ve usually lost your chance. But with a semi-auto, you can usually pop off that second shot during the first few seconds when they freeze up completely.
That said, most semi-auto owners that I know have them primarily for target shooting. A couple of the officers I work with are competitive marksmen even. One of them has an AR-15 that’s he’s put more money into for aftermarket parts than he did for the rifle itself. The other shoots 1911-style pistols. And there’s certainly some truth to the “tacti-cool” appearance being a motivating factor for buyers.
Powder load doesn’t really do that. It imparts velocity, which helps maintain accuracy over distance and gives penetrating power, but it doesn’t actually affect the damage done much. It’s the fact that the bullet is designed to tumble upon penetration that does damage. If the bullet didn’t tumble, you’d put a 5.56mm hole straight through something. But when the bullet tumbles, it creates a much, much bigger hole and has a much greater chance of hitting major organs or arteries. The alternative is having soft and/or hollow-point bullets that expand out and fragment on impact, which the Hague conventions have outlawed for military use, and which cause even more tissue damage. Which is why civilian rounds often still have the soft lead core partially exposed, but all military ammunition is what’s known as Full Metal Jackets, where the entire core is covered in a solid metal, usually copper. The FMJ penetrates really well, but tumbling isn’t guaranteed, and its penetrating power allows for overpenetration, meaning you’re more likely to hit something behind your intended target. Soft points don’t penetrate as well, and have much less chance of overpenetration, but they leave bits of themselves throughout the target and cause huge tissue damage because they’ll tumble, roll, and bounce around inside the target a lot more readily than an FMJ will. Which is why soft points are the preferred hunting ammunition - you’re pretty much guaranteed a kill through massive blood loss and high tissue damage if you hit anywhere in the main body of the animal.