I see all of these schools in Playbills, particularly Harvard, Yale, and Brown, plus a good amount of Princeton and recently a few Dartmouth. I think a huge amount of value at schools like these comes from the peer group, both while in college and in the form of further connections and professional collaboration. It is not just about the training, but also about spending four years training with people who will become playwrights, directors, and producers, in addition to actors. The creative team credits are usually where you find the most Ivy League grads.
To assess, I would try to find some current students at these schools who are either majoring in theater or who are heavily involved in theater and intend to pursue a theater career (and these people will not necessarily be majoring in theater). I would look closely at the curricula, but I would also consider the overall community and peer group.
In just this past month I have seen two Dartmouth grads perform in major roles at major regional theaters. I never thought of Dartmouth as a theater school, but both of these women were excellent. One is a very recent grad and does not have an MFA. The other does have an MFA.
As you presumably know, Harvard has just started its Theater concentration, so the program will be different going forward. It certainly looks promising. The curriculum at Brown (and Harvard) looks more performance-focused than Yale. I understand your son’s hesitation about Yale, but I would also consider that attending one of these schools as a theater major is about the connections, classmates, and community, in addition to the academic program. A lot of the performance opportunities at any of the schools you mention are student-driven, not curricular. Yale attracts more than its fair share of undergrads interested in theater.
Princeton does not have a theater major, and has a less artsy overall community than Brown, Yale, or Harvard, in my opinion. However, it’s more artsy than Dartmouth and closer to New York than any of the other schools you mention. There is definitely a strong core theater community there, and they are strengthening their program. I am “guessing” that a theater major may be in the works, especially because they are building a new performing arts complex.
I would guess that Yale won’t take an Arts Supplement because they get so many students applying who are interested in theater, and their academic program is more theoretical and less practical in orientation, making a supplement consisting of monologues somewhat irrelevant. Note that one can also get admitted to Northwestern’s highly regarded performance-based BA theater major without a supplement. I’m not sure I would let the non-acceptance of Arts Supplements alone sway him too much. The curriculum itself is another matter. There are real differences among the schools you list.
Also, I would suggest he think about the overall environment he prefers. This list of four includes a school in a fairly isolated, cold location (although with a cute town), a school in a suburban bucolic location with a cute town, and two schools in urban environments, only one of which is a major city. There will be a lot more opportunities to see professional theater on a regular basis in the urban/suburban locations.