The wire will not burn if the current is insufficient for the cable to act like a fuse or over heated resistor. It will heat and melt over a period of time with a certain value of over current, you are not running the PC long enough for that to happen, however it will still drop voltage over it's length and on a 3.3V rail you have very little margin before under-voltage is detected and the PSU or PC resets.
The wires are split to share the load as there can be very high currents involved and especially at lower voltages.
IE: 100Watts at 3.3 V is around 30A , at 12V it's only around 8A. That's why you need to have 2 or 3 feed through caps in parallel, each with an individual cable to load share the high current lines.