Odysseus was a cunning warrior and athlete, whom used his human talents to get home despite the enmity of Poseidon. Seems 5e doable.The casters can grow into any fantasy archetype - your wizard can become Merlin or Dumbledore. But, the non-magical types have a hard ceiling that they cannot ever be allowed to break through. You can be Conan or Aragorn, but, you can NEVER be Beowulf or Hercules, or Odysseus. Because anything that is outside the realm of the mundane can only ever be accomplished by magic.
But, a fighter that can swim across the ocean? Drink a lake dry? Leap across the tops of trees? Don't be daft. You can't do that without magic.
Conan, in the frozen land of Nordheim was the sole survivor of a battle of 80 men. Near unconscious Conan spied the scantily clad form of the daughter of the King of the Ice Giants, and pursued her across the frozen landscape until she called upon Ymir for rescue.
Rapey and distasteful....but doable by a high Con warrior against Exhaustion saves in 5e.
Beowulf- A peerless ( high stats) warrior with the Tavern Brawler feat, made a called shot after beating an Ogre into submission, and the DM allowed the player to rip the ogre’s arm off. It could happen at 1st level, with high stats and luck. Mr Bee-wolf also in the tales had a magic sword to kill the un-killable.
The heroes of myth were not made with the Standard Attribute Array....by mostly the heroes of myth are the extreme.
Best Longjumper in our world today, 29 feet. Str 20 Fighter... base of 20’....why can’t you leap from tree top to tree top.
Also, Magicians in myth are typically not the protagonist but NPCs.
Dumbledore was a NPC. Harry was a PC, he could cast Patronus , (essentially Prot from Evil), and ride a Magic Broom....but he was clever....and had Hermione and Snape. Ron just sucked.
Gandalf was a NPC- he died against a Balor. Merlin was a NPC, tricked by another NPC.
Egil of the Scandinavian Sagas was a warrior skald and skilled in runes, ( he cursed the king of Norway), so a Bard of the College of Valor could work, but again not many spellcasters appear as protagonists in the myths.
No one in 5e or life can drink an ocean, but with clever play and some plot devices, like in the myths it can easily be accomplished. I just do not find your argument holds water, no offense intended.