For amateur use, breakdown from overvoltage is probably not something you need to worry about. The main limits to power handling of a cable come from resistive heating and dielectric heating.
Arcing in coax is only going to be a problem for very low duty cycle applications, with modest average power and high peak power. Things like RADAR, where you have several kW but for only a few microseconds at a time, average power of tens or a hundred watts. Also for carrying DC power if that's your thing.
Well-specified cables have both specifications; let's take a look at an old favourite, LMR-400:
Its basic electrical specifications are pretty impressive when it comes to voltage:
2.5 kV between inner and outer. Also the DC resistance is amazing, a few ohms per kilometre!
But on page two, the power limits are much lower:
At 150 MHz, the 2 metre band, the average power it can carry is 1.5 kW, for an RMS voltage of 274 or a peak of 383 V, which is only 1/10th of the maximum DC voltage. This is for ideal conditions: stated as VSWR=1.0; Ambient = +40°C; Inner Conductor = 100°C (212°F); Sea Level; dry air; atmospheric pressure; no solar loading.
For infinity:1 SWR the voltage and current are doubled, (at different places on the line), meaning you have to reduce power by four times for the same heating (some assumptions!). You will also find the cable gets hot just in a few places, half a wavelength apart. I've felt this on RG316 cable at quite modest power, 10 watts or so.
The thermal time constant of the cable is probably longer than a second, so for morse code you could use the average power, not the peak. SSB also has a fairly high peak to average ratio, perhaps 4:1, again you could probably get away with using the average, as long as you never say "Haaaaaaaalo" for too long!
In summary, for high power operation, you need to choose a cable by its published power handling rating, not its DC spark-over voltage. Derate it by up to 4 times, if the SWR is going to be high, and some more for safety. Buy cables and connectors from a reputable manufacturer that has this detail on its datasheet.