There is no such thing as 'empty land'. Every square meter of Earth is part of some ecosystem that is under stress due to human activity. Solar and wind compound this problem.
>then reduce that to 30 to account for night-time
How about reduce that to 0 for night-time? I have yet to see a solar panel that works at night, or works well in cloud weather, or when covered by a layer of snow.
>Sounds like a lot, right? That's a rectangle 100 km by 300 km.
You missed some detail of land-use requirements in calculations. Like accounting for the battery technology that doesn't exist in order to bridge the intermittency of solar and wind. Also, even if this mythical battery technology existed, you would need to over-build wind and solar because after all, when the sun is shining you need to collect enough energy for right now + enough energy to save for later. Given that estimates say that we would need a minimum of few day (but more likely few weeks) of stored energy, for each day of power you generate, you need to over-generate a few days (or weeks) extra to store for later. Also, the population is growing. Our per-captia energy use is growing.
But let's set that aside. That is a lot of land. How can you say it's not!!!?? Every single one of those panels will be land-filled and replaced continually ... forever. So you have 100km x 300km (+ whatever materials you need to support and maintain those panels) of shit going to landfills that then you will need to subsequently dig up again to replace ... forever. And that's just one country. Our ecosystem is already stressed!