As other's commented it is "special" because a good portion of the radiation from the Sun is in the same range.

It's also special for a few other reasons. The most obvious one being that UV light is destructive to many forms of animal life, there isn't much utility in being able to see for example something like X-Rays. They don't occur naturally in any quantity and the mechanisms that create them (lightning) also give off visible light.

On the other end of things, lower energy photons are what we would call heat. Some animals can see it, but not humans. We can sense it just fine through other mechanisms however.

You're missing a big one: organic chemistry* changes often occur in the 4-7 eV range of energy, which is the visible spectrum.

* Meaning "molecules containing carbon", not "hippy chemistry done without pesticides".

This is all well and good, but the implication one level up was that there's a fundamental link between visible light and the energy levels involved in most low energy chemistry (or something).

Of course visible light is visible because it hits our eyes (is emitted by sun and is not filtered), but the comment about valence shells is quite a bit more fundamental than that.