Most starter motors or generators use turbine engines. These run with 30 volts without any sign of damage. When the starter is activated, an initial burst of amperage happens. In some cases, this can reach as high as 1000 amps. This represents a non negligible, and quite huge, current flow.
At startup, the motion is sustained. This means the amperage reduces massively throughout the startup process. Any battery connected will have to cope with this huge current change. Usually, the voltage is inversely proportional to the load applied. And this voltage has to be kept low to ensure that the turbines are started in the correct manner.
This is why Ground Power Units are used. At startup, the GPU sends 20% of the energy to the motor, thus facilitating the process. The GPU has a side effect of hindering the generation of heat which, in turn, increases the lifespan of the turbines.
In general, low battery voltage would translate to lower amounts of amperage. In fact, a few motors even bring down the batteries to a low 15 volts during the startup phase. One must be careful with these numbers though. As in most cases, especially in particularly sensitive industries, norms have to be respected. The industry standard for most companies is 28.5 volts during startup. This is a good compromise to effectively deal with the voltage drop.