When explaining this to people, we actually heard the argument, "But, what will she fill in the blanks for 'middle name' on government documents?"
Yeah, that's not a good enough reason for me.
I understand the middle name if you're trying to honor someone (but not honor them TOO much by giving them the first name). I understand the middle name if you want to be able to call them something different when you're especially angry with them. I understand the middle name to prevent confusion if your child's name is John Smith.
But, in all likelihood, our daughter is the only Daylia Olsen in the world. And there was no reason to give her one.