The history of the Internet explained how the Internet evolved along with its protocols. But it does not explain why an internetwork, instead of a specialized network, was needed by the Department of Defense.
The DOD was looking for a technology able to link all of its preexisting supercomputers and computer networks, using varied media for data transmission (ranging from conventional networking technologies to radio waves). This was a complex problem.
Networks are independent units. They consist of some computers, the hardware necessary to move information between them (lines, interfaces...), and some software to manage the links. This makes the physical and logical format of the data circulating on a network completely hardware dependent.
There is no simple solution to this problem, no possible dream of a universal standard for network hardware. The needs of two different networks can be very different, and often cannot be implemented using the same technology.
For example, for any transmission medium, there is a tradeoff between size and speed: a Local Area Network, linking computers in a single building, typically transmit data between 4Mb/s and 2Gb/s, while a Wide Area Network, which can span a continent, runs between 9,6Kb/s and 45Mb/s. (The technical choices are of course further limited by economic considerations: speed is always expensive).
All these practical facts explain why it was impossible to simply "plug" all the networks together. A new method had to be developed to interconnect heterogeneous hardware together: internetworking.