One problem with the SBSP concept is the cost of space launches and the amount of material that would need to be launched.
Much of the material launched need not be delivered to its eventual orbit immediately, which raises the possibility that high efficiency (but slower) engines could move SPS material from LEO to GEO at an acceptable cost. Examples include ion thrusters or nuclear propulsion.
To give an idea of the scale of the problem, assuming a solar panel mass of 20 kg per kilowatt (without considering the mass of the supporting structure, antenna, or any significant mass reduction of any focusing mirrors) a 4 GW power station would weigh about 80,000 metric tons, all of which would, in current circumstances, be launched from the Earth. This is, however, far from the state of the art for flown spacecraft, which as of 2015 was 150 W/kg (6.7 kg/kW), and improving rapidly. Very lightweight designs could likely achieve 1 kg/kW, meaning 4,000 metric tons for the solar panels for the same 4 GW capacity station. Beyond the mass of the panels, overhead (including boosting to the desired orbit and stationkeeping) must be added.
To these costs must be added the environmental impact of heavy space launch missions, if such costs are to be used in comparison to earth-based energy production. For comparison, the direct cost of a new coal or nuclear power plant ranges from $3 billion to $6 billion per GW (not including the full cost to the environment from  emissions or storage of spent nuclear fuel, respectively).