ABSORBER: Here's a good article on "green/yellow/red light" recruits from Tucker Frawley, Yale's RC.
https://www.frawleybaseball.co...e-Recruiting-Process
Most Ivies have about 7 likely letters per recruiting class, though some schools may be higher if they had attrition in their program. It's true that you don't receive it until around the time of the NLI date. (In some ways it represents a NLI, but with no $ attached, but a commitment).
And yes, the Ivies do look at the AI for each particular recruiting class. Your "answer" that you provided is not far from the mindset of the Ivies. HYP tend to have the smallest rosters. For what it's worth, there have also been sons of a number of former MLB players on the current rosters as of late.
Also, the number of PG commits listed can be under-represented for these reasons I know:
1) some don't do PG events
2) Some recruits waited until they got admitted, before they put the commitment on PG.
Good luck. I always say that several years back, Fenwaysouth called the Ivy recruiting process a "Labyrinth" of a process. Right he is, but worthwholeif you land a spot (see Goosegg's post) Good luck to your son.