From an employer's perspective, I think an elite college-only hiring strategy can work fine if the employer itself is prestigious or there's a clear unique value proposition there. For others, they're going to incur a negative selection penalty that may outweigh the signalling value that pedigree provides.
It's a Bayesian problem all the way through and you can probably quantify the value of the signal provided. However, and most importantly, it's just a signal. I personally prefer hiring interns, completely irregardless of school, and developing and hiring them, any time. At that point, there isn't signal, it's just measured performance that is de-risked.
Now, people that use it as credentialing are morons. I mean that bluntly and literally. Randomly picking on CFOs: "I want a CFO with a Harvard degree" is stupid thing to say, on its face. The person saying something like that has literally inverted the real point, which should be, "I want an excellent CFO, and a Harvard degree is a signal of some properties correlated with that outcome". Once you invert that, it's just another data point in a meritocratic decision, and a relatively minor one.
Sorry to post/write so much on this. Startups are the ultimate meritocracy in some ways, and having something posted here that's populist and almost anti-intellectual bothers me. Ycombinator has no problem pulling from Stanford. And Stanford, MIT, and Duke (and many others) are as elitist as any Ivy on any day that ends in y. That's leaving out the really class conscious "small liberal arts" colleges out there, and ignores the differences between ivy league schools in this regard, which is large.
"It's a Bayesian problem"
This we agree on. But we have to factor in adverse selection. If you're a prestigious employer, adverse selection is going to be small to non existent. The Harvard grads joining Dropbox are going to be all excellent. If you're a tier-2 employer with no particular unique value proposition, a Harvard grad that is willing to join you isn't the same thing as a randomly selected Harvard grad (unless there's a compelling reason why they would want to join), let alone the same thing as a Harvard grad entering Dropbox. There are selection effects working against you as an employer.
I've seen this personally, working at a little known company in a traditional industry without much to offer, we hired a Princeton grad who we eventually found out was fired from a few places and turned out to be worse than useless. We got adversely selected. They only wanted to join us (instead of a "better" company) because they were the bottom 10 percent of their cohort (not necessarily in terms of GPA, but in terms of ability to make themselves useful).
Useless people from Ivies are rare, but they do exist, and if you're an employer facing adverse selection you become much more likely to end up with one of those.
(Actually, I've worked with useless people from Cambridge, Tsinghua, and a few other elite colleges, many of whom we had to fire. The common theme was that they couldn't get into a better company, and so they joined us)