An ancillary cause of the decline of meter — or perhaps more accurately another symptom of the same set of transitions — is the increasing association of poetry with the plastic rather than the performance arts, and with the visual rather than the acoustical. This, too, begins with Plato.
Unless, of course, we can see it already in Pindar, inter alia:
Golden pillars we shall set up on the well-built porch
of the inner chamber and build, as it were, an admirable
hall, and from its inception we must make the face of the work
far-gleaming. (Olympian 6, 1-4)