Why do owners of airplanes need approval to fly? It's not like the air is owned by anyone?

Just because someone doesn't own something doesn't mean you can just launch stuff up there with no regard for other such things to be launched/already in the air. Things can and do collide, and the ramifications of that are actually much more dangerous when you don't have an atmosphere to pull the pieces down in the event of a collision.

The radio spectrum is limited, and belongs to the people. Careful regulation ensures it remains usable. Likewise, regulating orbits is important. For example, to limit potential damage from space debris.

For the communications, not the launch.

Political power comes from the barrel of a gun, and SpaceX is well within many country's sights.

e.g. that's the law.

But the path into space from the US is.

Governments are responsible for stuff launched into space form their territory.

When nobody owns something, we collectively own it. This means that we need to make sure that one bad, or reckless actor does not ruin it for everyone else. [1]

[1] https://en.wikipedia.org/wiki/Kessler_syndrome