He should absolutely apply SCEA to Yale. Why not? I would not recommend that he apply ED I anywhere unless there were a school that he likes as much as Yale and, if he were to be accepted ED I to whichever school that were, he would not be left wondering “what if?” or filled with "coulda, shoulda, woulda"s with respect to applying to Yale.
Has he visited and spent any time at Yale? What does he want to study?
Also, good advice to look into Rice. Their residential college system and “student happiness” rankings are second only to Yale. I’d also recommend looking at Wash U. and U.Chicago. (He can apply EDII to U.ChIcago if he doesn’t get into Yale SCEA where he to like it there.)
At the end of the day, what will really make or break his application are his essays and his teacher recommendations. Being able to show passion, wit, intelligence, and honesty are way more important than “padding” his resume with clubs. If he can tie in his passions – has he tried turning some of his “peer tutees” onto Shakespeare or done anything special with his tutoring that he can talk about? – so much the better! The fact that your son has done fewer activities but has done them consistently shows dedication and passion, traits that are way more important to Adcoms than membership in a gazillion school clubs.
What your son needs more than anything is to write some memorable essays (my D’s CA essay, among other things, was all about how Shakespeare had had a profound influence in her life [she, too, performed in a whole bunch of Shakespeare plays from 4th grade on, did summer Shakespeare Intensive conservatory programs for several years, etc.]; her longer essays and her 35 word short answers were witty and thoughtful; they supported interests that she discussed elsewhere without repeating information, and they showed a quirky, bright, interesting kid that can think outside the box.