To some degree, this is already done in the mobile manufacturing market. Resistors, capacitors, coils, and a few other basic components can be created by carving shapes into the copper using a laser instead of having to solder components onto the board.
I have to disagree with you on one of your points, namely:
Quote: "[...] and making it cheaper to manufacture."
Using a central chip instead of wiring everything directly would cost more to produce.
Anyway, my thoughts on this are that it wouldn't be of any use in mass production, and would be of little use for prototyping. There are two main reasons why I'd deny such a chip, speed and costs aside.
1) Your idea is flawed. You're not saving routes, you're actually producing more of them. Think about it, if I had a simple low pass filter (R series, C parallel), normally there would be 2 entries in the net list. But since you're connecting every component through a central IC, You'd effectively have 6 entries (worst case). So your idea of saving space is nothing more than an illusion, because every "pin" on every one of your components would have at least double the amount of connections to make.
Also, let me just put something into perspective for you. My current project has 576 entries in the net list, so your IC would need at least double the amount of pins. Not even an Intel i7 processor has that many pins.
2) ICs like this already exist. You named one yourself, FPGA. Another group that used to be used a lot are PLEs (programmable logic element) such as the GAL. They're pretty much obsolete now though, because micro controllers are cheaper and more dynamic.
These days, if you want to have a more dynamic circuit, the logical choice is to just use a micro controller. If the micro controller isn't fast enough, or a faster micro controller exceeds the cost of an FPGA or CPLD, those are the next choice in line.
In conclusion, there is no need to have the entire circuit dynamic, It's fine to hard-wire most of the circuit. You're never going to want to change the connections of, say, your voltage regulator, so there is no need for any more complexity.
The parts that do need to be dynamic are solved by using something along the lines of what you're thinking, a micro controller, FPGA or similar, but using this principle on the entire circuit would be an unnecessary waste of resources.
TheComet