Ralph McQuarrie is responsible for a lot of the designs in “Star Wars,” that of the stormtroopers included. Intriguingly, though, some of his early concept art for the original 1977 film features a stormtrooper wielding a lightsaber and carrying a shield as he faces down Chewbacca and Han Solo (who also wields a lightsaber).
Having swords and shields in space was not rare; it was a pretty common trope in science fiction in the ’50s and ’60s. Isaac Asimov, one of the biggest sci-fi writers of all time, introduced the idea of energy swords in space in his short story “The Traders” before later building upon it in “The Complete Adventures of Lucky Starr.” From “Buck Rogers” to “Dune,” many of the sci-fi works that eventually inspired “Star Wars” also featured swords in futuristic settings. “Dune,” in particular, found an elaborate way of justifying this by making projectile weapons ineffectual in its universe.
Eventually, Lucas would also scale down on the number of swords used in “Star Wars” by making them only available to Jedi. Why he took away the stormtroopers’ shields is another matter (though given how ineffective their armor is, they definitely could have used them).
Still, there is at least one stormtrooper who wields a lightsaber in canon. In the 2015 “Star Wars” Marvel comic book by Jason Aaron and Stuart Immonen, we are introduced to Sergeant Kreel, a member of Vader’s 501st Legion who fought Luke Skywalker with a lightsaber several times. Granted, he simply stole that lightsaber from a Hutt’s Jedi artifact collection and has no Jedi training, but it still counts!