question

Keep in mind also that the battery current isn't constant when inverting. The current drawn from the battery will roughly follow the AC current waveform. There are capacitors in the inverter that help smooth this but there will still be current variation at twice the line frequency (assuming single phase inverter system). I'm not sure how big this variation is but probably can't be ignored because Victron makes an issue of ripple battery voltage. Unfiltered, the peak to average would be about 50%. Average 12 volt current with a 3000 watt load with 95% inverter efficiency would be approximately 3000 / 12 / 95% = 260 amps and peak current could be 50% larger than that: 390 amps. The peak is certainly much less due to the inverter's internal capacitors. Keeping resistance in the battery path to a minimum is the goal to minimize battery voltage ripple as much as making sure the average current doesn't cause an excessive temperature increase in the cables.

So Victron's cable sizing addresses all these issues. If your system loads are less than the 3000 watts, then things (including wire sizing) could be scaled back. But in the grand scheme of things wire is relatively inexpensive and overdesign will insure the system works in the worst case conditions.