Some of my free-verse, like the poetry that people (in comments on the above links) are referring to as "prose with random line-breaks", has random-seeming line-breaks because that is how my brain works and that is how the words come out. I rarely edit my free-verse because it is self-descriptive in that way. The form of the stream-of-consciousness describes the words as such.
I love reading. Anything with words on it. Poetry, prose, cereal packets, anything. I initially had difficulty reading haiku, for example, because I could not "feel" the meter but now love to read and write them because they tickle the mathematical part of my brain much like knitting does. There is bound to be a poem or poetry style out there that I cannot parse but I can usually eventually see the meter, rhyme or lack thereof as part of the meaning of the poem.
Maybe it is because I have a classical music training as well. Many of my poems I have set to music with my guitar, back when I still used to play, and so know that much poetry (and even prose) can have rhythm imposed upon it by setting it to music. Just because the author did not make it blatantly obvious to the reader with signposts, rhymes, line-breaks and other punctuation does not mean that it is not there to be found.
I used to hate "poetry appreciation" classes at 'high-school' in English Literature class because, as someone who had been writing poetry since I was eight, I knew that the reader would very often have no idea what the author meant by their poem's words. I went through a phase of writing poems as opaque and hard to decipher as possible that were also 'clever', 'pretty', lyrical or rhythmic, just to see what other people might (fail to) make of them. I knew what I meant by them. They were my own secret code to myself, I suppose. I remember verbally laying into one English teacher (6th form, my friend's (who talked me into showing him my poetry) teacher - I did not study English) who had offered to critique some of my poetry out of class. He had talked about how I should edit them or change things. He just did not get that the words came out of my head, off the pen and onto the page (in those days - keyboard, often, now but more rarely) exactly how I meant them to be. Changing them would ruin them and change what they were saying. Narcissistic of me, maybe, but if the words asked me to write them, who was I to change them?