How does the modernist drive toward innovation in Western culture coexist with the use of ancient myths in T.S. Eliot's The Waste Land?

Modernism, as exemplified by The Waste Land, is the product of an irredeemably fractured society. In the years following the First World War, when the poem was written, many of the old certainties had vanished. The rise of mass society, with its extension of the franchise and its democratization of culture, had undermined the traditional foundations of Western civilization.
However, even Eliot realizes that there is no going back. There is no way we can recover the old myths and the lost classical heritage of a bygone age. They are gone forever, destroyed by the disruptive spirit of the democratic age with its dynamism and ceaseless innovation. As a consequence, the voice of authority has been undermined in politics, society, and culture alike. This explains the fractured nature of the many voices we hear throughout The Waste Land. There is no one voice—nor can there be. There is simply a mixture of voices, each uncomfortably coexisting together in an "unreal city," which could be anywhere or nowhere. In such a fractured world, it no longer matters:

What is the city over the mountainsCracks and reforms and bursts in the violet airFalling towers Jerusalem Athens AlexandriaVienna London Unreal.

Where once the voice of Western culture displayed such a remarkable degree of unity, especially in the Middle Ages, now it has been broken down into a collection of little voices, each occupying their own little world, without any means of coming together to form a coherent culture.

Le Prince d'Aquitaine a la tour abolieThese fragments I have shored against my ruins.

"The Prince of Aquitaine in the ruined tower." Eliot is like the prince standing high up inside the crumbling tower, the tower of Western high culture, and he is casting a mordant eye at the titular waste land around him. That culture is broken; all that can now be done is to collect the various fragments of broken myth littered throughout the poem and use them to create a testimony to a vanished world.