Why (if anything) is a planet clearing its neighborhood important?

[Lord Torath]

Not quite:

Where is the Barycenter of the Earth and Moon system?

This is the case for the Earth–Moon system, in which the barycenter is located on average 4,671 km (2,902 mi) from Earth’s center, 75% of Earth’s radius of 6,378 km (3,963 mi). When the two bodies are of similar masses, the barycenter will generally be located between them and both bodies will orbit around it.

But Pluto and Charon orbit a barycenter that is well outside of Pluto.
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