Your son should apply to Yale in the SCEA round!
FWIW: Like your son, mine was white, had a 36 ACT with a 4.0 unweighted GPA. Unlike your son, mine didn’t have any legacy status. Unlike your son, mine was ranked about 20th in a class of 900 students. Unlike your son, mine went to a feeder high school (Stuyvesant). Like your son, mine was involved in sports (baseball) for 20+ hours a week – with a 20-game fall season, winter workouts, and a 36-game spring season. Like your son, mine was NOT Div 1 talent. Like your son, mine was so involved with sports, he didn’t have time for volunteering, charity work, or other “high profile” high school activities.
Never-the-less, my son applied in the SCEA round, and wrote his essay about his baseball coach and all the life lessons he learned from a man who did not attend college. He was accepted in December of 2011, graduated with honors in 2015, and had the absolute BEST time of his life at Yale (playing for 2 years on Yale’s club sport baseball team – the JV league).
Although Admissions Officers say “We look at applications holistically”, a 36 ACT (which is rare) seems to put students at the top of the admit pile, no matter whether they apply in the SCEA or RD round. Given all of the above, your son should apply to Yale in the SCEA round and see what happens. Best of luck to him (and you)!