Hydrostatic equilibrium is the most defensible of the requirements to be a planet.

The IAU wording is, "...has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape."

In this case it just means that the planet's mass and therefore gravity is sufficient to give it a spheroidal shape. (Technically the equilibrium is with the opposing push from the planet's material, which resists gravity's attempts to compress it. The result is a sphere, made spheroidal in real planets by rotation.)

Less massive objects like asteroids can have weird shapes, like the asteroid Toutatis which has a sort of dumbbell / unshelled peanut shape. The hydrostatic equibrium requirement prevents such objects from being classified as planets, as well as small objects that just happen to be round for other reasons.

This isn't really social history but simply classifying the objects according to intrinsic properties, which seems fine to me. This classification could be applied to objects anywhere in the universe without any problem.

The other two requirements are more problematic and arbitrary. One is that it has "cleared its orbit". Earth, let alone Mercury, would be unlikely to qualify for this if it were at the same distance as Pluto, for example. Rogue planets also can't satisfy this one, and we've observed those.

The other is that it has to be in direct orbit around the Sun, not a satellite of some other object. This excludes exoplanets as well as rogue planets. The rationale for this is that they didn't have enough observational info to say much about exoplanets, but that seems like a flimsy excuse. A good definition would apply to exoplanets by virtue of being theoretically sound, and not having been tuned to fit the way they were trying to classify solar system planets.

> Less massive objects like asteroids can have weird shapes, like the asteroid Toutatis which has a sort of dumbbell / unshelled peanut shape. The hydrostatic equibrium requirement prevents such objects from being classified as planets, as well as small objects that just happen to be round for other reasons.

Okay, and how did you arrive at the hydrostatic equilibrium requirement? What law of nature told you that planets must be spheroidal?

You're only adding this requirement so the outcome fits your pre-existing desired results, since you're literally arguing for the requirement based on what objects it excludes. And what are the consequences of such arbitrary decisions, according to you? "You can't get away with that in, say, physics and still end up with useful theories[...]"

Do you get the issue with this line of critique? There is literally no useful definition of "planet" that is non-arbitrary.