We have to look at an example including the cables resistance. I assume 0.05 Ω for both legs. If the load is 100 A for one leg only, the voltage drop at the cable is 5 V and we loose 500 W in the cable. If the load is 50 A for one leg only, we get a drop of 2.5 V and a cable loss of 125 W. If both legs are loaded with 50 A each, the loss in the cables is 250 W only. But we have to pay for all power what is used after the companys power meter. In both cases we pay for 12 kW, but we can use 11.5 kW with unbalanced load and 11.75 kW with balanced load.
But the cables between the center tapped transformer and the secondary windings of the transformer have a resistance too. The same is true for those, the balanced loss is smaller than the unbalanced one. If the power company installed a power meter with extra charges for unbalanced loads, you pay a little more money for the unbalanced 12 kW load. But a suitable extra charge is not unfair, without it the customers with better balanced loads have to pay for the losses caused by customers with unbalanced loads.
If there is one single large load like a washing machine, it is better to use a machine for 240 V and 10 A instead of one with 120 V and 20 A. A loads using 240 V will be balanced by itself.