Anything that is a sphere and orbits a star is a planet. Asteroids don't have sphere shape. Same goes for comets.
Ceres and Vesta are nearly spherical, yet are asteroids. Do they get counted as planets too? (They used to be.)
You're right that the definition was tailored to keep the number of defined "planets" within reason. There was no way to include Pluto in this category and NOT include Eris, Haumea, Makemake, etc., so the definition was tailored to exclude them. It also happens to exclude Ceres and Vesta, though it wouldn't be a huge problem if they were considered planets (as they are the only two members of their class).