There are plenty of semi automatics that are developed for hunting. The modern version of the Browning BAR, Remington 7400, Benelli semi-auto shotguns we're all developed to for use in hunting.

There are a lot of good reasons to use a semi-automatic fronting. Considering that semi automatics are just as accurate as Bolt actions at typical hunting ranges I can't really think of a reason why I would not use a semi-automatic. Usually when you miss while hunting you don't completely miss the animal. You just missed the vital Zone. That is where the semi-automatic really shines cuz you can get a much quicker follow-up shot at the vital zone.

It was pretty common practice when people were primarily using bolt actions to go hunting with another person. That person would also point that rifle at the game in case the primary shooter misses the first shot but still hits the game animal.