A Direct Box has a single purpose: to match impedance levels between devices. Guitars, basses, keyboards, and other instruments typically output signals that are expected to be sent to an instrument amplifier. If you send these to a recording device instead, the results are low signal and noise from the mismatched impedance. The noise is not as noticeable going *from* an instrument to a recording device. However, taking a recording device's output to an instrument-level amplifier will demonstrate the noise quality quite noticeably. (There are re-amping boxes available, which are pretty much reverse DIs.)

So, a DI is not exactly substituted for patch cable length, since it is providing a valuable electrical manipulation. Remember, audio signals on a wire are represented by electricity. Learn more about basic electronics and you will have a better understanding of the fundamentals of why a Direct Box is utilized.