I'll agree with that statement. But the one single thing that draws the most and determines the limits is cranking and to a lesser extent firing of the injectors while cranking.
Look at it this way, if cranking a large bore diesel in cold draws the system voltage down to ~6 volts, that has cut the system in 1/2. a 24 volt system that looses 6 volts while cranking is still at 18 volts. It is all about getting the truck running, once that is done, the alternator carries the load.
You can afford to loose 6 volts with a 24 volt system, you can not with a 12. Injector firing is done at a much higher voltage on the new trucks, then system voltage. If the system is pulled too low it can't even fire the injector even if the engine is cranking fast enough to start.
It is becoming more and more common on newer vehicles to have charging voltage controlled by the ECM in order to quickly replace what was drawn off when the vehicle was shut down.
Storage batteries (common lead acid types) can provide small amounts of current for a long time but are extremely limited in how large a current draw they can provide for even a short time. It isn't a liner graph. A Maxwell supercapacitor can provide enough current to start a big bore diesel in -25F in the form factor of one Gp 31 battery, but can be totally depleted in 25-35 min by connecting a single headlight across it. It is the opposite of a battery, the Maxwell can supply huge amounts of current for a short period. It does not store more energy than even a single group 31, but can release it all at once. This is proven by the fact a single gp 31 can recharge the Maxwell multiple times (charging current for the Maxwell is less than 18 amps)
Key off loads could be handled by 4 lead acid batteries in parallel and carry that load for a week or more, but not be able to crank the engine in the cold because the current draw exceeds the ability of the battery to provide, either provide more, or reduce the current needed. doubling the voltage cuts the current in 1/2. doubling the voltage does not increase the total capacity in watt/hrs of the system. You are still storing the same amount of energy, but can better access the stored energy when a brief large draw is on the system.
I don't claim to be schooled on the latest, but the laws of chemistry and physics don't change. I do have an fair but by no means complete understanding of the modern systems on vehicles. I am by no means an expert.
By raising the voltage, you are reducing the current required, and current is the limiting factor. Once the truck is running the charging system supplies not only the current to keep it running but also the current to replace what was used to start.