Why does melted chocolate that is simply cooled back down often fail to regain a shiny professional finish?

Answer: The fat cools into a messy mix of crystal shapes that scatter light

The fat cools into a messy mix of crystal shapes that scatter light ✓ — Correct. Tempering builds a tight network of stable crystal forms, and that network is what gives chocolate its gloss and snap. Melt it and let it cool on its own, and the fat locks into a loose mix of forms that scatter light instead of reflecting it. The cooling path matters as much as the final temperature.

Cocoa butter rises to the surface and sets as a dull, streaky layer — Fat bloom does look like a dull, streaky surface, so this is a fair guess. That bloom comes from cocoa butter migrating to the outside over time, not from a quick melt-and-cool at home. Here the trouble is inside the bar, where the crystal forms never get organized.

Moisture dissolves surface sugar and leaves it as a rough, grainy layer — Sugar bloom is real, and it does leave a rough, sandy surface. It happens when moisture dissolves sugar and then the water leaves and the sugar recrystallizes. Simple cooling trouble is about fat crystals, though, and the surface here is dull rather than gritty.