If there were as many private helicopters and planes as there are cars, helicopters and planes would not be safe anymore. Even with fancy antigravity technology. You simply can't have flying things in city streets. If things go wrong, you have cars crashing into the 50th floor of a building, or dropping straight on the ground on people from 200 meters.
I don't think we're anywhere near having things flying around inside urban canyons.
Air traffic works the way it does because it is dominantly a public transport that takes place mostly outside the cities.
Outside the cities, yes. Dominantly a public transport? That depends on how you define it. In terms of person-miles flown, sure. In terms of pure number of aircraft
, maybe not. There are a *lot* of private planes up there. Still nowhere near as many as there are cars on the ground, but they tend to outnumber the commercial aircraft in many areas on a nice day. (In the weather, things change a bit.)