Power is volts times amps (Watts = V x A). So if you have a lot of voltages you don't need many amperes. Roughly you need 18 times as much current from 12 volt battery as you need from 220 volt AC outlet. Current is what causes cables to heat up, not voltage. That is why they use thousands of volts in power transmission grids. The thing to do when you have lots of current is to lower resistance of cable. The larger the wire, the lower the resistance. Think of cable as a water pipe. A big pipe (wire) can carry more water (current or amperage) with less pressure (voltage), and will present less pressure (voltage) drop from one end of to the other.

Another consideration is how far cable has to run from battery to inverter/UPS. Long cable runs are expensive, either in copper or efficiency, or both.