Does brewing hot chocolate for longer hours make a difference?
Cacao powder is not very soluble in water, so I'm gonna go out on a limb here and guess that the extra time allows for the cacao to incorporate better into the liquid.

The recipe includes actual chocolate nibs, but after it's melted into the milk / cream there's no extra flavor infusion by keeping it for a longer time.

12 hours sound like a lot: if you keep the mixture cold, it takes longer to dissolve (but not that long); if you keep it warm there's a risk of spoiling the milk. I can't think of a benefit to let the drink sit for such a long time.