Unrhymed poetry is not a 20th century invention (all ancient poetry was unrhymed).
John Milton, Paradise Lost:

THE VERSE
The Measure is English Heroic Verse without Rime, as that of Homer in Greek, and Virgil in Latin; Rime being no necessary Adjunct or true Ornament of Poem or good Verse, in longer Works especially, but the Invention of a barbarous Age, to set off wretched matter and lame Meeter; grac’t indeed since by the use of some famous modern Poets, carried away by Custom, but much to thir own vexation, hindrance, and constraint to express many things otherwise, and for the most part worse then else they would have exprest them. Not without cause therefore some both Italian, and Spanish Poets of prime note have rejected Rime both in longer and shorter Works, as have also long since our best English Tragedies, as a thing of itself, to all judicious ears, triveal and of no true musical delight; which consists onely in apt Numbers, fit quantity of Syllables, and the sense variously drawn out from one Verse into another, not in the jingling sound of like endings, a fault avoyded by the learned Ancients both in Poetry and all good Oratory. This neglect then of Rime so little is to be taken for a defect, though it may seem so perhaps to vulgar Readers, that it rather is to be esteem’d an example set, the first in English, of ancient liberty recover’d to Heroic Poem from the troublesom and modern bondage of Rimeing.

There is a funny passage in Goethe's Dichtung und Wahrheit about his father's prejudice against unrhymed poetry.