There are semi-auto hunting shotguns aplenty. They usually only have 5-shot magazines, though. Even in NJ, most sport shops have a few AR-15s available, though you can only get 10-shot mags in this state. But most states still allow hi-capacity mags like 30-shot ones, since the useles Clinton ban lapsed. The AR-15 is the single most popular rifle purchased in the US, so there's no shortage of them.
handgun today is a 9mm semi-auto with a magazine of 12-15 rounds. Go to any sporting goods store and the handgun case will have more semi-autos than revolvers. It's simply what modern guns are.