Several things....
1. As someone said, ANYTHING can be set to music. I set Lincoln's Gettysburg Address to music. Interestingly enough, I can (for the most part) SING it from memory, but cannot quote it from memory. Eventually, I used the music for something else.... a song called "All Done Believin."
2. Your lyric EASILY accepts music. I was able to sing it with a fairly dramatic vocal melody on first read. It wouldn't be much work to fit it to existing music OR to write new music for it. You've done a good job of keeping a cadence.
3. I'm going to disagree that a song "MUST" have structural integrity throughout. They usually do, but that's usually because musicians insist on it, and have been trained to consider it necessary.
There ARE exceptions.
4. It's easiest to simply give in and format the structure to fit existing criteria/rules. But the world won't end if you don't, and it really does NOT make it overly difficult to fit music to the lyrics. Since you are submitting to a critique that will come mostly from musicians, I would suggest that you re-format your lyric to fit the "rule." But if you feel strongly about not doing so, it's YOUR song.
Most memorable songs ARE memorable because they "violate" one "rule" or another. There are better rules to "violate" than the "structural integrity" rule.