I would like to point out the complexity involved in organising flight levels for the relatively minor number of planes in any given local airspaces, and how many flight controllers are required.
Now I would like to point out the fact that if you add more planes/flying cars to organise to flight levels, you will increase the number of controllers. And at the moment, computers can not do this. At all. For just the planes. This creates a lot of stress on the people controlling, and stressed people make mistakes. There will be a lot more accidents than a simple linear extrapolation would indicate.
Now, the other thing I'd like to point out is the immense complexity with flying something like a plane. My younger brother is a pilot, and to fly something as simple as a little cessna is a year long training course, that is extremely difficult, and requires an aptitude test to actually get into, much like any medical profession. Flying the plane, even after this, is still incredibly complex at any given time. There is a reason there are that many switches in a cockpit.
So, I'd like to conclude that the vast majority of people are simply incapable of flying, and if we did open up the airspace, the strain on organisation would be so huge that we wouldn't be flying long. Ergo, flying cars are dumb.