Love your metaphor about Daedalus but labyrinths have a single path compared to mazes which have multiple branching paths.
From Wikipedia: https://en.wikipedia.org/wiki/Labyrinth
"Although early Cretan coins occasionally exhibit branching (multicursal) patterns,[2] the single-path (unicursal) seven-course "Classical" design without branching or dead ends became associated with the Labyrinth on coins as early as 430 BC,[3] and similar non-branching patterns became widely used as visual representations of the Labyrinth – even though both logic and literary descriptions make it clear that the Minotaur was trapped in a complex branching maze."
If the cretan Labyrinth didn't have branching paths, why would Theseus need a ball of thread to retrace his steps? https://en.wikipedia.org/wiki/Ariadne#Minos_and_Theseus