[univacky]

That's not true for many, many planes, and there are very many private planes that are not jets and the owners are not rich. Thousands and thousands are homebuilts.

Go to https://www.faa.gov, and on the front page there's a place to enter an airplane registration number and get, along with other info, the name and address of the owner.

The vast majority of airspace does not "require very clear tracking of objects", and is less controlled than a highway. It does not require particular permission besides following the "rules of the road", and is free to use with nobody knowing you're there. I must assume you are referring to airspace which is either around busy airports (cities) or very high (airliner territory) - Class A/B/C/D airspaces.