The only time I'll use higher magnification is when shooting paper targets, or possible shooting varmints or big game at extremely long range. Over the years, most of my personal hunting handguns have been scope with Simmons handgun scopes. Mag revolvers that use red dot sights. They come in handy when hunting at close range, and where having to make a quick shot such as hunting wild hogs with the aid of dogs. I have also used Bushnell's Holosights under those same circumstances and found them to work extremely well.
Many states allow hunting with handguns during the regular firearm seasons.
However regulations regarding what handguns can be used, calibers and case design and other restrictions vary from state to state. Before going afield to hunt with a handgun always first check with that state's regulations.