It's a little more involved than just the power supply being unable to provide the current to double the power as load is halved. You can design two amplifiers with the same power rating at 8 ohms and have one being able to double power at 4 ohms and the other with the power remaining the same. Yet the amp that doubles the power can sound worse regardless of its heftier power supply and yet have nothing to do with the quality of the components.
When a speaker draws current, the power supply gets taxed. If the power supply serves both the input and output stages, the voltage sag affects both. This will cause the input stage to distort which sends a distorted signal to the output stage which then gets amplified to the speaker.
However, if you split that power supply with two stages of regulation (expensive), then the current demanded by the speaker only goes through the output stages, leaving the input alone. The input signal is left undisturbed by voltage fluctuations but the output power delivery is limited. So that's one answer as to where the "missing power has gone".
Another answer is that the power supply may have the capability, but poor design (such as high impedance) may cause the power supply to waste heat, thus robbing the output stages of the ability to maintain voltage during speaker impedance dips. There are other reasons, but basically the missing power is either diverted for better fidelity, is wasted as heat or is simply a victim of the manufacturer's budget.
When a speaker draws current, the power supply gets taxed. If the power supply serves both the input and output stages, the voltage sag affects both. This will cause the input stage to distort which sends a distorted signal to the output stage which then gets amplified to the speaker.
However, if you split that power supply with two stages of regulation (expensive), then the current demanded by the speaker only goes through the output stages, leaving the input alone. The input signal is left undisturbed by voltage fluctuations but the output power delivery is limited. So that's one answer as to where the "missing power has gone".
Another answer is that the power supply may have the capability, but poor design (such as high impedance) may cause the power supply to waste heat, thus robbing the output stages of the ability to maintain voltage during speaker impedance dips. There are other reasons, but basically the missing power is either diverted for better fidelity, is wasted as heat or is simply a victim of the manufacturer's budget.