I have no idea of where the idea of poetry without rhythm or without rhyme originated. I suspect it might have been with Walt Whitman. Whitman used a very loose rhythm in his lines. Sometimes he used rhymes ("O Captain! my Captain! our fearful trip is done;/The ship has weather’d every rack, the prize we sought is won..."). Sometimes he didn't (I sing the Body electric;/The armies of those I love engirth me, and I engirth them;/They will not let me off till I go with them, respond to them,/And discorrupt them, and charge them full with the charge of the Soul..."). I tend to like Whitman's poetry when his rhythms are a bit tighter and he utilises rhyme. I tend to dislike Whitman's poetry when his rhythms are loose (or non-existent) and he does not utilise rhyme. Unfortunately, it seems to me that Whitman's poems with loose or non-existent rhythms and without rhyme have been the most influential. At the very least, it seems to me the majority of modern poets follow their lead.
Personally, I would rather modern poets look to Lord Byron or Edgar Allan Poe for inspiration. Both Byron and Poe were masters at rhythm and rhyme. And they were both capable of the most beautiful imagery to be found in poetry. If I were to create a list of the greatest poems of all time, both Byron's "She Walks in Beauty" and Poe's "Annabell Lee" would rank in the top ten.
Of course, I don't want it to sound as if I believe that rhyme is all important to poetry. In the poetry of various ancient, Germanic peoples, alliteration rather than "end rhyme" was used in poetry. The perfect example of this is the Old English poem Beowulf . In the original language it is absolutely beautiful. Another example is the collection of Old Norse poems known as the
Indeed, I suspect that the reason poetry is not as popular as it once was is that, at least to me, it seems as if most modern poems have very little, if any structure. Among the ancient, Germanic peoples, poetry was probably the most popular art. It continued to be popular into the Middle Ages, into the Renaissance, and well into the 19th century. It seems no coincidence to me that poetry declined in popularity in the 20th century when "free verse" became the norm. I very seriously doubt that many people today read poetry at all.
My hope is that a new Byron or a new Poe will arise, someone who does not write in free verse, someone who writes real poetry. Maybe then future poets can throw off the legacy of Whitman and poetry will once more become a popular art.