Unless the chain gets contaminated with a lot of outside dirt (like riding in sandy or muddy conditions), the majority of the black contaminant in the cleaning solvent is very, very fine metal particles from the chain. These disperse in the chain lube to form a colloid, which makes the lube more pasty, plus also acts as an abrasive. You can find proof of this by dipping a magnet into the used cleaning solvent, it will emerge covered in sludge, and sand and dirt are silica and organic matter, not ferromagnetic. This is why the lubricating oil gets black so quickly after cleaning, no way to avoid that, I only clean my chain when the level of contamination makes the lube thick and pasty. That's with liquid lube.

Melted wax, on the other hand, one that is hard at room temperature, tends to not hold metal contaminants; Either the wax keeps the metal parts separated, or when the wax wears through and you get metal-to-metal contact, the fine metal powder seems to self-shed by gravity into the environment, without sticking to the wax. When you rewax the chain, you will see very little contaminents, a bit over time, but nothing like with liquid lubes. You can even remove the contaminants from the wax by melting it with some water present (added before heating up, not added to hot wax), the wax will float over the water, leaving behind the contaminants in the water after the wax cools, according to someone on the forum (I have not yet tried, I do have an old puck of candle wax with a small amount of metal on the bottom, after like a decade of use).