When John sat down to write "Imagine" in 1971, he had moved far away from his "Dylanesque" period of obscure references and deliberately confusing imagery. His songwriting had evolved through primal scream therapy, in which he was forced to strip away his defenses and truly feel all the pain he had buried since childhood.
Even before the therapy brought this newfound cathartic songwriting style to its peak, however, he was already on his way. When talking to Jann Wenner about the John Lennon/Plastic Ono Band album (the one that took shape post-primal scream), he said:
I remember that the simplicity on the new album was evident on the Beatles double album [The White Album]. It was evident in "She's So Heavy," in fact a reviewer wrote of "She's So Heavy," "He seems to have lost his talent for lyrics, it's so simple and boring." "She's So Heavy" was about Yoko. When it gets down to it, like she said, when you're drowning you don't say, "I would be incredibly pleased if someone would have the foresight to notice me drowning and come and help me," you just scream. And in "She's So Heavy," I just sang "I want you, I want you so bad, she's so heavy, I want you," like that. I started simplifying my lyrics then, on the double album. (Source)
Every bit of anger, hurt, love, sexual impulse, bitterness, jealousy, and regret that he had ever felt and buried came flooding to the surface and began to shape his songwriting as he matured. By the time he got to Imagine, Lennon had reached a calm after the storm and was ready to take this simplicity to a higher, philosophical level. The inspiration for the lyrics of "Imagine" was Grapefruit, a book of instructional poems by Yoko Ono. Shortly after the two met, Yoko gave John a copy of her book. At first, he didn't really understand the point of these poems that were usually just based around one word, but gradually began to appreciate them.
The first line of the book is, "Burn this book after you read it," and John's contribution is, "This is the greatest book I've ever burned." John recalled:
She gave me her "Grapefruit" book and I used to read it and sometimes I'd get very annoyed by it; it would say things like "paint until you drop dead" or "bleed" and then sometimes I'd be very enlightened by it and I went through all the changes that people go through with her work—sometimes I'd have it by the bed and I'd open it and it would say something nice and it would be alright and then it would say something heavy and I wouldn't like it… I would start looking at her book and that but I wasn't quite aware what was happening to me and then she did a thing called Dance Event where different cards kept coming through the door everyday saying "Breathe" and "Dance" and "Watch all the lights until dawn," and they upset me or made me happy depending on how I felt. (Source)
Still, "Imagine" wasn't his lyrical best. As Philip Norman points out, "With Paul looking over his shoulder, one cannot picture him rhyming 'isn't hard to do' and 'no religion too,' or repeating the same word ['one'] in the chorus. The little falsetto 'You-oo' he uses as a bridge to the chorus seems too poppy—too Beatly—for such elevated subject matter." (Source)
But perhaps that's the point. Perhaps "Imagine" needs to be appreciated with the same bare simplicity of these instructional poems. We're asked to envision a world free from suffering, and it's a beautiful thought no matter how far-fetched or naive it might be. As far as cohesiveness is concerned, Lennon really does model his lyrics around the poetry; "imagine" is the central verb and there's no central image, but rather an abstraction upon which the rest of the lyrics are built.
If you think about it, some of the most enduring and affecting poems in the English language are just a few simple words. The "imagist" movement in modern poetry is representative of this idea, though it focused on concrete images instead of philosophical ideas. Poets like Ezra Pound and William Carlos Williams led this movement and were able to create a huge feeling and capture the essence of something with just a few words. Check out "In a Station of the Metro" or "The Red Wheelbarrow" if you want to see an example of this.
As Lennon told Pete Hamill in 1975, part of the reason he left the Beatles was because he felt their songwriting had lost its poetic quality:
It became journalism and not poetry. And I basically feel that I'm a poet. Even if it does go ba-deeble, eedle, eedle, it, da-deedle, deedle, it. I'm not a formalized poet, I have no education, so I have to write in the simplest forms usually. And I realized that over a period of time… I realized that we were poets but we were really folk poets, and rock and roll was folk poetry—I've always felt that. Rock and roll was folk music. (Source)