To say it correctly, it is because it is making more power, not just more amps.
Just in general, think of it like this:
The amp's outputs have a maximum voltage that can be present before clipping.
Voltage = current * resistance, so with a set voltage, if the impedance drops, the current increases.
Power = voltage * current, so more current = more power.
Now regardless of output current, voltage, or whatever impedance is on the output, you just need to know how much power is on the output. The power in = power out divided by the efficency.
Power = current * voltage, the input is 14.4 volts, so you can determine the current.
If the amp is 1000 watts, and it is 80% efficent, then it has to have 1250 (1000/.8) watts at the input. At 14.4 volts, it needs 87 amps to make 1000 watts on the output. Noticed I never had to know the load or output current to determine that; It does not matter if that is 1000 watts at 4 ohms, or 1000 watts at 1 ohm.
As already stated, the big factor is that the amp's efficency is going to change as the load impedance drops. From the formulas above, if the efficency changes with different loads, the input current will not be a linear relationship. And just as a side note, a lot of amps to not actually double their output when the load impedance is cut in half.
In your example, the amp may need 50 amps with the 4 ohm load, but it may need 110 amps with the 2 ohm load, and it may not actually make double the power on the output.
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