Why Amateur transmitters, transceivers, SWR meters, amplifiers and most antennas are all designed around a 50 ohm system, so the standard coax for ham use is 50 ohm cable such as RG-58, RG-8X, RG-8 and LMR-400. Matching the feed line impedance to the equipment keeps SWR low and power transfer efficient. The other common coax impedance in the world, 75 ohms, is the television and video standard, not the ham standard.
Watch out 600 ohms is roughly the characteristic impedance of open-wire or ladder line, a balanced feed line, not coax. The very low values like 8 or 12 ohms are not standard transmission line impedances at all.
Ham radio runs on 50: 50 ohm rigs, 50 ohm coax. 75 ohms is for TV, 600 ohms is ladder line.