The amount of solar energy that strikes the Earth is irrelevant. Superman only has access to the energy that strikes Superman. That gives him access to the energy of a single solar panel, or a small bush.
It shouldn’t be necessary to do the math. Anyone who spends 5 minutes outside should have a rough idea of how much energy strikes a human
being. (Were you instantantly incinerated? No? Can Superman incinerate a large boulder with heat vision? Yes? Gee, wouldn’t it take at least a few weeks to accumulate that much energy?)
But let’s do the math anyway:
At this distance, the sun provides about 1353 W/m^2 of power in space. On Earth, you have to divide by 4 because about half the energy is
reflected by clouds, and another half is lost at night. Toss in a reasonable estimate of 100 cm^2 for the surface area of Superman’s face and hands (which are the parts he normally exposes), and you get 33.8 Watts. Call it about 30 Watts if you want to account for the fact that Superman must reflect *some* light, or he’d be jet black.
So the next time you see a 30-Watt light bulb, just think: that’s how much power Superman has access to. If he stores it like a battery, he should be able to lift a 1-ton car a couple of hundred feet into the air once per day, or a major feat (such as the ship he lifted in MOS #2) once every 20 years or so. Logically, Superman’s batteries should have been depleted after his first week on the job.
In the case of Superman, I’d say the “solar battery” people are squarely in the “less complicated” camp. Accepting an obviously-false explanation is less scientific than saying, “Kryptonians get superpowers under a yellow sun, and nobody knows why”.
In the case of Spider-Man, I’m torn. On the face of it, spider venom shouldn’t have any more connections to a spider’s abilities than, say, snake venom. So why didn’t Peter get snake powers instead? The whole bit about “it was a spider, therefore you get spider-like powers” does have a hint of sympathetic magic about it.
Frankly, I find it hard to be too worried about it. As far as I’m concerned, Spider-Man’s origin has nothing to do with how he got his powers — the spider bite is the McGuffin part of the story. His *real* origin is when he found out who murdered Uncle Ben.