Worse yet, we have not just specialized, we have lost knowledge as well. My favorite example of this is a result I rediscovered. Every mathematician knows that, for instance, sqrt(2)+cube_root(3) must be the root of some polynomial of degree 6. (This one turns out to be x^6 - 6x^4 -6x^3 + 12x^2 - 36x + 1.) I came up with a construction for answering questions like this. I showed it to a number of mathematicians, and none had seen it until I showed an older one who said, "That looks like a very old way to do this. Go to the library, pick up an algebra book from the 1800s, and see if you find it."
I did, it was there, and it turns out that two of the mathematicians I had talked to were in fields that had gotten their start from the very construction I rediscovered! (One was in number theory, dealing with things like algebraic integers. The other was in combinatorics, and did a lot of stuff with symmetric polynomials.)
If you're curious, the observation behind the construction is that any polynomial expression that is symmetric in the roots of a polynomial can be rewritten as a polynomial in the coefficients of that polynomial. So if a1 and a2 are the roots of x^2-2, and b1, b2, b3 are the roots of x^3-3, then (x-a1-b1)(x-a1-b2)(x-a1-b3)(x-a2-b1)(x-a2-b2)(x-a2-b3) is a polynomial in x and the coefficients of x^2-2 and x^3-3, which means that it is an integer polynomial.
All that said, this point doesn't support your argument. It is true that if information were better presented, people could learn more about more subjects than they could otherwise. It is true that trying to do this would have tremendous value. But if you want to learn about multiple subjects then you need to deal with how information actually exists out there in the world, rather than how we'd like it to be organized. The disorganization that you point to is a significant barrier to learning. (This problem does not look like it will improve any time soon.)
As it is, tons of stuff keeps getting reinvented just because the state of the literature is so bad that you'll never find it, unless it was invented exactly in your sub-sub-specialty, or you serendipitously found it via a colleague who remarked that what you were doing sounded similar to something he once read.
The decline in scientists writing books also doesn't help. It used to be that prominent scientists would gather up their scattered papers and unify them into a magnum opus laying out their theories, or possibly a few different books, one on each major area they worked on. That sometimes happens, especially in areas like cosmology, but it's much less the norm than it was 100 years ago. Today it's quite common to just publish 200+ papers over your career and not really do any summarization of them, even though there is plenty that could often be done, since it's common for papers to supersede or overlap with previous ones.
Actually, on that front, it'd be a big win if scientists with lots of publications simply provided some sort of brief guide to them. Take the 50 papers on lasers, and provide an annotated bibliography explaining which papers are the important ones, which papers are obsolete or superseded, and which ones might be of particular interest to people working on particular topics. A few people do that, but many don't even separate their list of publications by topic, let alone provide a guide.
Or, shorter: There is a lot of stuff published, but it's terribly indexed and summarized, which I think is a bigger problem than the volume alone.