Traditional power stations aren't exactly small, either. In fact, people will think you're a lunatic if you start talking about nuclear or coal in "per square meter of land" terms.

Think I point out is there is a perception issue. When people thing 'power plant' they think of a large concrete building with a bunch of machines in it. But they don't think of all of the supporting infrastructure. (Comment I've heard about nuclear power in France is on hot days it's partly limited by the need to avoid dumping too much waste heat into the rivers. Coal fired plants seem neat and tidy until one thinks of the strip mines. Gas fired, the massive network of pipes needed to extract the gas and move it to where it'll be burned.

For context: my local nuclear power station is about 600 W/m^2, unless you count the purpose-built lake it relies on for cooling water, in which case it's 50 W/m^2. The 17 W/m^2 estimate above for solar doesn't look as bad as I would've guessed.