I don't think we need more so-called interdisciplinaries (at least any more than we need regular old physicists and sociologists), I think we need people who learn primarily the big-picture framework of ideas. When searching for a solution to some technological problem in today's ultra-fragmented and specialized world, each person working on the problem will start with what they know and go in the most promising direction from there. Eventually they come to some conclusion, using the knowledge in the local neighborhood of their own specialty. People are amazingly resourceful, so a little bit of localized knowledge is enough to hack together some solution.
Starting a search from a random point will only lead you to a local maximum. Sure, if you start the search from a whole bunch of random points (like hundreds of researchers in different fields working on the same problem) you'll find a global maximum eventually, but that's not always possible, and it's never efficient. If there were people who were trained to know just what knowledge exists rather than all the details and methods of applying it, they could point in the right direction to start with.
Even group work doesn't replace this kind of skill. The only specialized scientists who can speak with each other are in close enough disciplines to share a jargon. That's hardly a broader view of the world of science.
In the age of the internet we're becoming familiar with this need even on an individual level. Knowing how to google things is more important than knowing things. Knowing what research exists is just about the most important first step when starting a related research project. There's no longer any point to memorizing details, nor is it even possible to learn as many details about any particular thing as people used to, when the subject goes so much deeper in any direction. It's far more important to learn the epistemological structure of those details in order to build up a greater understanding.