I think we'll see solar power in space with transmission to earth around the same time as we have an operative space elevator. Solar power on earth is just too cheap, relative to the cost of launching things into space for the forseeable future.
I saw a theoretical study someone put together for a space elevator. You need a material that is at least four times the strength of carbon nanotubes for it to be possible at all, and if it ever fails or gets damaged it has the potential to wipe out all life on the planet as it wraps itself around the equator with far more force than an asteroid impact.
I agree the core points if both your post and the one above it - space based solar can deliver massively greater amounts of per unit area (which is what the OP asked,) but we would need a much cheaper way of getting it to orbit for that to make any kind of sense.
At this point, we don't need that kind of power, anyway - current generation solar panels located in and near habitable areas could easily meet our total demand annually - though we'd need a whole lot of storage and/or a lot more transmission capacity to make it practical.
Walter