I just had a weird idea, maybe “Isn’t it Ironic?” is meta. That is it’s ironic that none of the examples in the song are what most people would consider ironic.
The third post kind of hints at that but, yes, one of the tongue-in-cheek analyses of the song is that the title is ironic itself, a sort of meta-irony, as you note. I remember reading a story somewhere about Alanis where a fan came up to her and asked her if the title was supposed to be ironic and Alanis just kind of agreed. (Possibly apocryphal, and her agreement does not mean it was intentional, if this story was true. It’s pretty clear to me that she was [mis]using the word in its very loose colloquial sense.)