I think the institution I'd want to go to,and the one that creates the most educational value overall, would be one that tries to find a good balance between the two types (and while there won't be many ideal types and most people will be on a spectrum blah blah! I think most people in the ability range were talking about will veer clearly towards one or the other).
I do not think that an institution who tries to limit type b to only 10 percent of candidates will create as much overall educational value as one that moves the percentage closer to 50. Having pointy types dominate might not be good for either type of student.
I really think this "two types" thing is a complete myth.
Why?
Polymaths certainly exist, and those who excel at a single preferred domain also do. The two general groups of individuals do sort of form a mutually exclusive pair of sets. Granted, there are probably some people who trend one way or the other without being at either extreme, but among gifties, it doesn't seem to me to be a grossly controversial statement to note that most tend to be one or the other.
So there are children who take college coursework in one domain as quite young kids-- those would be the pointy ones. There are also children like my DD, who is entering college years before her peers (though she wouldn't have been ready
quite as young as a "pointy" peer-- perhaps 12-13yo rather than 6 or 7), and is seemingly "very good" at everything she has ever done-- but doesn't yet for-sure-for-sure have a major picked out, and keenly feels that she isn't "extraordinary at any one thing."
She is right about that-- she isn't. She's very good at
everything. But she is also a lot more comfortable to be around for most people than super-pointy types who are VERY good at a single domain and may only be "adequate" or even just "good" at other things.
It's not clear to me what the right proportion of the two basic tendencies is "right" for an institution of higher learning, but clearly such institutions have an unstated desire to produce "rounded" education in their graduates, else general education requirements for degrees would not exist. I have seen quite a few VERY brilliant students struggle with some elements of such general education requirements, for whatever that is worth-- the pointy ones sometimes can, in a relative weakness.
The bottom line is that BOTH types look identical via the imperfect and not-terribly-difficult testing that is currently used to winnow the field of applicants. Test them both at age 18 with the SAT, and on any given day, perfect scores are as likely as not.
By that measure, they are both "highly qualified" for elite institutions.