There IS private airspace indoors (it is why drone races typically happen in warehouses or stadiums). Outdoors, there is no private airspace so much as there is Class G airspace which is all airspace under 1200ft as long as you are out of range of any landing strips/airports, or under 700AGL if you are near certain larger airports. It is not legal to fly any manned aircraft in class g unless either transiting through to land/takeoff, or if you have clearance. However, it happens fairly often (just look at sightseeing helicopters as an example). A common problem with drone hobbyists is that they don't know anything about commercial airspace. Much of the concern has been about flying near airports where transiting low-altitude space is necessary. If drone operators had been assiduous in avoiding those areas (as RC aircraft operators have been) then this would be less of a concern.

I agree though, that there is very little possibility of enforcing low altitude airspace rules, unless they force some kind of software/transponder system into use. even then, the home-built drones are just too easy to make to guarantee it.