Yes we tell these tales, but each tale still has a bit of "innate magic" to why impossible things happen.
Er...no? I specifically cited several of these examples because they DON'T have that. Beowulf. Atalanta. Liu Bu. Rostam. Odysseus. They are literally just
really badass mortals. Odysseus is technically the great-grandson of a god, namely Hermes, but he is never at any point characterized as even remotely divine. And literally everyone on that list
is not divine. They weren't gods, they weren't demigods, they weren't special inherently magical people. Some are heirs of kings, others aren't. Some are great generals, others aren't. Some were world-class athletes, others weren't. Beowulf stands out especially, since he gloats about doing things like swimming for five or six days straight
in full battle armor, and then dives to the bottom of the lake where Grendel's Mother lives...taking HOURS to reach it while holding his breath the whole time.
All of them were people whose skill or strength transcended the limits of what should normally be possible.
Without magic of any kind.
Now if you're suggesting every warrior who takes the "divert river" ability is part demigod, I'll gladly accept it.
Nope! I think people who are 100% purely skill-and-strength type characters can become just so. gorram. GOOD. at what they do, they genuinely pass beyond the limits of the mundane, without becoming "gods" to any extent or "innately magic" or whatever else.
It's called becoming "transmundane" (not a term I invented, but the term I choose to use for this). And yes, it
absolutely does have backing in the context of
specifically European myth, legend, and folklore. Beowulf, who delays his own death from a
mortal neck wound for hours just because he wants to see the treasure
and its reburial before he dies. Atalanta, faster than any living human being, just because she'd been raised by motherflippin' bears. Liu Bu, throwing a spear that could kill an enemy commander from a mile away. Odysseus, so cunning and guileful that
even his enemies celebrated him as, in Latin,
Ulixes sapientissimus graecorum: "Ulysses, craftiest of Greeks" ("sapientissimus" literally means "wisest", but the more accurate translation in this context is "craftiest").
And beyond that, you have things like the "riddle of steel", the blacksmith whose works are magical despite he himself knowing no magic, the bazillion Plucky Upstart Children who survive harrowing experiences with nothing more than some cleverness, tenacity, and audacity.
Purely "martial" character doing "impossible" things is alive and well in fully authentic European tales.