No, they definitely have been known to overhunt; it's just that it's not really worth your time to hunt something inedible, unless you're after its fur (wolf and wolverine fur, for instance, doesn't ice up when you breathe on it), and if it's not bothering you. There's also the matter of the large, heavier carnivores simply being difficult and dangerous to kill, even with many men and dogs, when you only have stone-tipped weapons. It's the exact same reason wolves don't generally go out of their way to wipe out every bear, lynx and mountain lion in their territory, if their pups aren't being preyed upon. Them merely being competition isn't worth the trouble and risk.

Once you start investing your time and effort into raising and feeding livestock, however, the game totally changes, and rather than viewing the preds as mere competition, they now become thieves, and a whole different sort of psychology comes in. Also, the advent of metal-tipped spears and arrows helped a lot in humans becoming more pro-active in defending themselves and their herds (by calling for bounties, the oldest known one on wolves (golden "jackals") dates back to ancient Egypt. Oh, and when it comes to the difference between stone and metal arrowheads? The fletchers of Europe enjoyed about a hundred years of their trade being relevant than they otherwise would have done, thanks to North American natives being hot on them; until guns got better, the fur trade was mainly about them finding that steel arrowheads were far superior to stone ones, and helped them get rid of those pesky white bears all along the St Lawrence that they had previously been terrified of ... and made good trade on their skins in the process.)