It's the other way round. At low speed, you don't need a high voltage on the battery for high phase amps, as the BEMF is low. The voltage difference between BEMF and battery voltage has to be high enough to drive high currents. High voltage only helps for higher speed, not for more torque at low speed.
A different thing is the max battery current. With P=U*I, of course you need less battery current for the same power with higher voltage and you run into the battery current limitation at higher power.
With full throttle, you are hanging in the phase current limitation normally at low speed, at higher speed in the battery current limitation.
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