A science question

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Put another way; our vision system has adapted to work well with solar radiation

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It's not just that solar radiation peaks around visible frequencies: our atmosphere also has a (fairly) narrow window of transparency in the same region.

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While acknowleding the various complexities you mention about how heat is transported; we do know from the large temperature gradient that Earth is radiating more energy than it receives.

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While this is a reasonable conclusion, do note that it does not actually follow rigorously. The sun is also radiating more energy than it receives, but it has the reverse temperature gradient, at least in the chromosphere and corona. That is, the temperature rises with increasing distance from the center of the sun.