We should just be called moons of the Sun then. And then call the Sun the moon of the...Milky Way.
Stars have different physical properties than planets. The reason we give different names to various celestial bodies is because of the significance of those differences, and, equally, the uniqueness of all these classes of difference. It's the same thing as giving a different word to all the various types of food, rather than just saying "I'll have some food for dinner." There are some kinds of food you won't eat, can't digest, or wouldn't want. "Celestial bodies," likewise, is a good term for emphasizing that asteroids and supernovae have something in common, but without a functional nomenclature to communicate the important unique qualities of all the celestial bodies out there, we cannot proceed in our scientific discourse.
That's why the Pluto case was so important. As our astronomical observation capabilities have improved, the number of known objects in the universe has increased, blurring some of the old distinctions we use to make between "celestial bodies." Now, newer distinctions evidence themselves. This is scientific progress in its purest form. I was proud of these scientists for going against what they knew would be a strong cultural inertia and classifying Pluto not as the planet we have all grown to think of it, but as the planetoid (or dwarf planet, if you like) that it more properly
is. In science, reality must eventually win...or it's not science.
In fact, the romance with which we view planets is more properly a game of perception. The fact that Pluto's fate is being received by the public in a way exemplified by this topic, is more a ballet of human psychology than a serious astronomic debate.