I'm not talking about self-taught vs. college educated. Computer science can be self-taught. You can buy all the books at a regular bookstore and you don't need special lab equipment or anything. If you're a self-taught developer with a passion for the profession and you're a good learner, you'll probably end up learning some CS along the way.
I still don't see a correlation (we certainly agree on whether a particular slip of paper is useful), so let's turn it around: what is it about computer science (in the realm of Big-O, lambda calculus, Turing machines, discrete mathematics, and such [obviously I've left a bunch out and intentionally started on the more theoretical. Feel free to ground me in somewhat more useful CS.]) that you think makes for better developers?
I totally agree that an attitude of self-teaching makes better developers. There is a lot in the application of CS, but I would call that Software Engineering.
Well there's breadth of expertise. Part of CS is systems, which includes networking, operating systems, compilers, and so forth. If you're making any of those things or leaning heavily on them, you want to hire people who are grounded in those fields. Same goes for things like AI, machine learning, data mining, and so forth.
More generally, having seen more kinds of software kind of broadens one's way of approaching programming problems, so even if you don't directly use anything you see when you study operating systems or compilers or AI, you can grab vague approaches and ideas from those fields.
If you're interested in writing performant software, you'll care about big-O, algorithms, and data structures. Understanding algorithms and data structures enables you to intelligently choose and apply them even if you don't have to develop them from scratch.
