That definition means a planet has nothing to do with physical state, and everything to do with the proximity of your neighbors. We could promote the Moon to a planet by pushing it further away, or demote Earth from being a planet by slinging it a bit closer to it's hungry uncle Jupiter. We could demote all planets by extinguishing the Sun! Then the entire system stops working and it's all just asteroid or something.

That arbitrarily chosen definition doesn't describe the object, only it's place in the malleable hierarchy. With this, the title of planet tells us nothing about the object itself, except that it's orbit is only dominated by a star.

Even worse, the IAU definition is extra arbitrary, as it only counts objects that orbit specifically the Sun, so the vast majority of bodies in hydrostatic equilibrium that don't fuse hydrogen aren't planets. They also play very lose with hydrostatic equilibrium, as Mercury isn't in hydrostatic equilibrium, yet is explicitly classified as a planet. And "clearing it's orbit" is also rather indistinct, with no method to determine this is given. It's up to argument if Neptune is a planet, as many plutoids intersect it's orbit.

Even more worse, the barycentre of our solar system is sometimes outside of the sun! That means sometimes the Sun is co-orbiting with the rest of the solar system bodies, and therefore by this definition nothing is a planet! It's a definition so arbitrary that it periodically stops existing!

I'm not just saying I disagree with the IAU here, but that their definitely is objectively poor, and poorly used. I agree that Pluto, Eris, Ceres, and many others should be in a different category from Jupiter, but make some categories that make sense, please!