The IAU did come up with a boundary: having enough mass to clear (most of) its orbit. That's because simply mass and roundness are pretty arbitrary numbers that could be set to anything, while clearing the orbit is decently well-defined, at least mostly. It's a good post to set as the lower limit for the mass of planets. That's why Ceres is no longer considered a planet as well, there's millions of asteroids in the Asteroid belt and it's not massive enough to get rid of them. Similar reasoning goes for Pluto, Eris, Makemake, and their friends in the Kuiper belt. They're not massive enough to clear their orbits of all those asteroids and other small objects.

Well orbits and neighbours and such I would argue is very important in astronomy. If you were all alone in the void of space and there is nothing else that exist, there wouldn't be anything to compare against. The idea of relative size, mass, rotation, position, and even time wouldn't really exist. The whole idea of moons is that it orbits planets, no matter its size, composition, or mass as long as it was naturally formed (hence why the ISS is not considered a moon, it's an artificial satellite). Planets, by definition, are objects that orbit stars. Moons don't orbit stars and hence cannot be planets.

I'm not very good with analogies, but here me out. Imagine the hands of a clock, all alone with no clock for the hands to tick. They may as well be pointy bits of metal, they are not hands without the clock. Just as moons are but rocks when without a planet, or how planets are not so without a star.