At the college level, private schools certainly do cater to the individual. I was fast in math, regular speed in everything else. They put me into grad level math and physics classes, while my writing/history/etc classes were still at the normal pace.

I don't see much reason why the incentives would be different below the college level.

Whenever you want to ask "what would a privatized primary education system do", you can often ask instead "what does the privatized secondary education system currently do?"