First, it would be impossible to prohibit any type of airplane from flying over private property. Especially with the widespread adoption of GPS in the cockpit, hitting the "direct" button and just going rather than navigating the airway system is becoming increasingly common, especially under visual flight rules (which any LSA would probably be using). What restricted airspace there is already makes things difficult for pilots; making the space above every house restricted up to FL180 would just be insane.
However, there is a regulation specifying certain minimum altitudes over congested areas, which theoretically ought to give the pilot of a stricken aircraft enough time to glide somewhere relatively open for a forced landing.
Second, what we're talking about here is really more of a "road-worthy airplane" than a "flying car". The implication is different. Cars are something everyone has; airplanes are more exclusive. The addition of the LSAs above to the skies would not present any particular threat beyond that already posed by the many small private aircraft up there, because they'll still be fairly exclusive and require significant training to operate. It's not like you're suddenly going to be handed the keys to an airplane with no flight training.
I read recently that the entire General Aviation community uses as much fuel in a year as American automobiles do in a day. There's still a huge gap in relative numbers.
There's a big push right now to get more people into flight schools, however, and these new toys and LSAs in general may help to do that.