Well, I’m Protestant, and I agree with you about why the poem’s theology is wrong, I just also happen to disagree with you about praying for the dead.
That being said, pretty much my entire family is Catholic, and I’ve attended plenty of Catholic funeral services where the priest assured the assembled family that their departed loved one was in a better place. Maybe the priests didn’t really believe that theologically, but I think, in that situation, both Protestants and Catholics tend to care more about comforting the grieving than being theologically accurate.
Several years ago I had to have a fairly minor surgical procedure. I went to confession before hand and told my priest that if anything should happen that he was not to say that I was in a better place. I told him instead I wanted him to say that if I was lucky I made it to purgatory. He told me he would keep that in mind.