It makes moon a planet, unless you want to include parameters like “must orbit a star”. but that seems arbitrary.

This is the core conceptual and historical distinction between a moon and a planet. If your definition of moon doesn’t include the moon, our moon, Luna, you’ve fucked up.

The concept of a planet is about orbits. That’s what the word means; the wandering points of light in the night sky. Moons don’t wander separately from their planet. Dwarf planets aren’t points of light distinct from the rest of the asteroid belt they’re in.