Why A transceiver on transmit can draw tens of amps (a 100 W HF radio pulls roughly 20-25 A at 13.8 V). Any resistance in the power leads drops voltage according to Ohm's law, V = I x R, and that drop grows with current, so the radio may see too little voltage and produce distorted audio or shut down. Short runs of heavy-gauge wire keep resistance low so the full supply voltage reaches the radio under load.
Watch out Impedance matching applies to RF feed lines, not DC power wiring; a DC supply should have very low source impedance, not one matched to the load. Radiation and RF interference on DC leads are handled with bypassing, ferrites and bonding, not by wire gauge.
DC power leads are about current, not RF: short and fat means less voltage drop under key-down load.