If you set the thing up in the L1 Lagrange point it will have the same day/night problem that traditional solar has. You would need at least two, but probably realistically 3 different antenna farms to collect the power and the satellite would need to be able to track the beam across the surface of the Earth. Most of the proposals I've seen have the array in geosynchronous orbit so it can easily remain pointed at a fixed spot on the Earth.
You could also beam power from L1 to geosynchronous orbit and then to a single ground station. It really depends on how efficiently you can beam power, but hitting Type 1 on the Kardashev scale hits limitations based on radiative cooling into space vs incoming energy.
However, it makes sense to have hundreds of ground stations simply to minimize transmission losses on the ground. And presumably utilizing ground stations 24/7 is vastly less critical than maximizing the return on space based infrastructure.
One could put SBSP at the Earth-Sun L2 point, and just use ground based solar during the day. Weirdly, this would mean in winter at high latitudes one would mostly be getting solar power at night!
At the distance of the L2 point laser power beaming would probably be necessary to keep the transmitter and receiver sufficiently small.
