I mean, I don't think Tolkien is a great example since his characters tend to be capable of ridiculous feats, like Fingolfin (an elf) crippling Morgoth (Satan) and Ecthelion (another elf) killing multiple Balrogs (devils) by himself. Smaug was slain by a single archer, and any "noble" warrior in Tolkien's world can kill dozens of orcs. Tolkien did not abide by medieval realism to the extent that modern authors do.
You are talking respectively about an angelic figure wounding Satan, another angelic figure killing lower devils, an archer accomplishing a purely aiming feat against a weak spot he was given special knowledge of, and high level warriors slaying runts with inferior equipment (Tolkien standard orcs are rather smaller than humans, and when one of them has almost human size, like the one in Moria, you see the trouble he creates).
Magic in western culture is typically something only employed by the bad guys (am I right,
ERYFKRAD ?), and that has nothing to do with wargames. What modern/contemporary fantasy and videogames have done is to extend the Gandalf archetype to humans (because magic is cool and opens up more possibilities), and make it a common occurrence. There is a reason why there is only one good wizard in Tolkien (Radagadst is much more of a Konrad Lorenz type, the Blue Istari are MIA), he is not human at all, and even he uses his magic very sparingly.
In this respect, Battle Brothers is a very old fashioned game: there is magic, but only evil guys/non-human beings have access to it. The main characters have to go through obstacles with steel and grit (and the odd suspicious beverage or mushroom).