Conan himself has a bit of plot armor due to being the main protagonist, but, even so, REH writes in a way that makes it at least seem as though Conan could die or be hurt. There are also limits to what even Conan can do. While he might be able to fight several foes and win, he's still not tanking armies. In some ways, Conan himself is a plot device to help illustrate how serious of a threat other things are. He's described as this muscled man of immense strength, so when a demonic creature or beast threatens to overpower him, it helps to illustrate the seriousness of the danger posed.
Even so, there is a sim aspect to REH's writing because a lot of things just kinda make sense. Even Conan needs an army to fight an army. It's not uncommon for a wizard trying to cast some elaborate and time-consuming spell to just be stabbed as a way of stopping it; in contrast, when powerful magic does actually happen, it carries a lot of weight.