The term "planet" is poorly defined - well, more contrived as it has no basis in anything other than itself. Generally, good schemas derive from properties in more generic schemas, they're constructed from something rigorous. Poor definitions exist to collect unlike things that are convenient to distinguish.

One thing we know about good definitions is that if you apply some transform t() to a thing to change it into another thing, there is a corresponding transform of similar nature, t'(), that applies to the nomenclature. If you have a triangle and add a side, you get a quadrangle. If you take the ingredients for a cake and follow the recipe, you get a cake. You can produce diagrams that show the one-way and two-way relationships.

For the current definitions of asteroid, planet and comet, you can't do this. You need external parameters that are arbitrary, and you cannot say in advance if a relationship is one-way or two-way because the definitions refer to properties wholly unconnected to the object.

That's not good reasoning. Nor is it acceptable to define the maximum permitted number of planets. We do not limit the number of cities in countries, or the number of countries, to suit school geography grades.

No, we need something better.

There are a number of definitely topologically distinct objects in a solar system. There are objects with no structure, they're grains held by gravity with no adhesion beyond that. There are objects with no core, they're homogeneous. There are heterogeneous objects sorted by mass. There are heterogeneous objects that are unsorted. Both have one core. Then there are objects with multiple cores.

Some objects are child objects, spawned from another. Our moon is one. Many small asteroids have evaporated and recondensed, so are not primordial. Ceres seems to be a captured comet.

These may not be the attributes you'd use, but they show intrinsic attributes exist and can be used. Such properties will be true for all observers for a meaningful length of time. So why not start by forgetting a meeting of the IAU that may have violated quorum rules and decide what is intrinsic enough to satisfy a planetary scientist, cosmologist or astronomer as being useful to everyone?