Your entire analysis is very flawed. One, in the 18th centry 90% of the time your shooting and melee infantry are the same unit. And it takes time to switch. Two, his army was heavy on the cavalry so he could take out the AI fast. He zipped in his light cavalry to pounce on the enemy infantry before they could fix bayonettes and form a square. Which is what they are for, and you'll note he took some heavy losses in the light horse units. Three, firing through your own lines with muskets is, simply put, not possible.

He saw that the AI was going to assume a defesive posture, as he had the high ground. He used his light cavalry to delay that until his infantry were in range. Then it was all over.