Is it ironic that...

I'm totally good with you using the song as a demonstration of what is or is not ironic. I use this song in my own classes. However, I believe you've made an error in saying that there is NO irony in the song. There is one instance. The verse about Mr. Play It Safe, includes one ironic statement. When she says, "and as the plane crashed down, he thought, 'Well, isn't this nice.'" The "Well, isn't this nice" is verbal irony. He is saying the opposite of what he means, which I assume would be something like "Oh, holy obscenity, I'm going to die." Verbal irony certainly exists, because people say it does. But we should probably be calling this sarcasm.