A bit like the dilemma when you realise Ironic by Alanis Morissette contains absolutely no irony....You're most right, but there's one exception in one of the verses:
"Mr. Play It Safe was afraid to fly
He packed his suitcase and kissed his kids goodbye
He waited his whole damn life to take that flight
And as the plane crashed down he thought
"Well isn't this nice..."
And isn't it ironic... don't you think"
Yes, Alanis, that would indeed be ironic. Most of the other lyrics are implied/potential irony. "Rain on your wedding day" would be ironic if every day surrounding it had been glorious sunshine. "Good advice that you just didn't take" is only ironic if you'd taken and fallen for countless pieces of bad advice. I'm with you though, taken without those assumptions the song does rather fall down! :0)
Why look, it's a blog: