I find it particularly amusing that the IAU definition, in a footnote, expressly declares the eight planets to be what they are. In other words, the true definition for being a planet is to be defined as a planet- so the criteria it gives are entirely superfluous, at least when it comes to our own solar system.

It's clear that they worked backwards from the eight planets to come up with a classification system that fit, but in realizing the problems with the approach, just gave up and created the carve-out.

Also, just as another example of the absurdity of the IAU definition, there's a pretty strong argument to be made that Earth's moon would be a planet under the criteria: it orbits the sun, it's round, and it's massive enough / positioned such that it's capable of clearing its neighborhood.

It orbits the Earth rather than the Sun by most conventional definitions of the word, although apparently the IAU doesn't have an official definition of orbit that I can find.