What you refer to is called "power supply droop" and is mostly due to the limited size of the power transformer. It takes a large transformer to be able to maintain a high enough regulation factor to handle a full doubling into 4 ohms - and a large transformer costs lots of money.
As to whether this doubling always correlates with better sound, I have doubts. There are numerous design issues that also need to be considered, such as the power supply rail voltages and the current load on the transformer, not to mention the circuit topology and gain devices. In my experience, there is little correlation between power output and sound quality so long as the amp is powerful enough for the chosen speaker.
Arthur
As to whether this doubling always correlates with better sound, I have doubts. There are numerous design issues that also need to be considered, such as the power supply rail voltages and the current load on the transformer, not to mention the circuit topology and gain devices. In my experience, there is little correlation between power output and sound quality so long as the amp is powerful enough for the chosen speaker.
Arthur