The gaps easily get canceled out by using newer solar panels; I took the low end of commercial solar power outputs I found on the web, many of the more recent ones do 20W/sq foot or more. 25% gaps seems generous.

I thought about the rare-earth issue, but there's a simple solution that bypasses both it and the energy-storage issue: use solar-thermal plants instead of photovoltaics. These require only mirrors and steam turbines, both made out of abundant materials. Efficiency is actually higher than photovoltaics (30% or so), and energy can be stored as heat for up to 5 hours before it's used. (Ironically, they have the same issues relative to photovoltaics that photovoltaics have over fossil fuels; in theory they're simpler and more environmentally friendly, but implementing the theory correctly requires solving a number of engineering problems that together make them cost more and generate more hiccups than photovoltaics have.)

The higher cost isn't actually true anymore, for photovoltaics and wind at least. Solar hit grid parity with fossil fuels in late 2015, and is now actually cheaper than coal power plants. This (rather than subsidies) is why the coal industry is in deep shit: it just doesn't make economic sense anymore, and the electric industry is rapidly switching over to renewables & natural gas.