The rationale for limiting the allowable launch azimuths for many launch sites usually includes "dropping booster stages on population". With SpaceX (and maybe Blue Origin in the future) returning first stages to the Earth in a controlled manner, does this (or should it) change the allowable launch azimuths available to operators?
The FAA, by rule, requires an exclusion for any air space over which a rocket is flying with its Flight Termination System armed. I guess they consider that the FTS might actually be used, in which case rocket pieces may be traveling in an uncontrolled way. Since Falcon 9’s 2nd stage FTS isn’t safed until well after stage separation, I think that’s enough to keep them flying over the usual controllable ranges.
For more discussion on logic behind this, see the FAA's Notice of Rulemaking section 5:
For a launch vehicle that uses a flight safety system to ensure public safety, a launch operator would establish flight control lines that border populated and other areas requiring protection. By implementing flight safety limits and flight termination rules, a launch operator would keep debris created by a malfunctioning launch vehicle from impacting any populated or other protected area outside the flight control lines. ... The flight safety limits would account for the errors and dispersions associated with the launch vehicle and flight safety system, which includes the flight termination sequence of events.
One of the proposed criteria for establishing flight control lines dictates that flight control lines must protect any land area not controlled by the launch operator. The FAA's protected areas would not only include towns, cities and other obviously populated areas, but all land areas outside the control of the launch operator because of the relatively high probability that people could be present on any land and the fact that any land may constitute property or contain the property of others. The safety of ships and aircraft would be addressed through the establishment of hazard areas and flight commit criteria as discussed earlier in this notice.
There is some discussion of how to handle "application of risk assessment techniques to quantify the risk to people in a proposed land overflight for purposes of determining whether the risk remains within acceptable limits" but the standards are very high:
For example, the FAA expects that no launch in the foreseeable future would be able to meet the E C criteria of 30×10−6 if the planned trajectory involved placing a gate in a flight control line that would result in overflight of a city or other densely populated area.
Bob's answer seems correct and covers the legal aspect, but it might be useful to note from an engineering point of view the conclusion is also correct. In particular that even when things go well: booster stages fall out of the sky, is only part of the issue. If it was all of it, we could have solved the problem already anyway.
For example, its not super hard to predict the landing site of a rocket for which all is going well, without the extent of active control necessary for self landing. The restriction applies because of the propensity of things to not go well. The hardware and software that allows a landing, doesn't really effect what can go wrong in flight, nor how it is capable of dealing with an issue.