The idea that doubling power is important springs from the concept that loudspeakers are ’voltage driven’. What this means isn’t that the speaker is driven by voltage (despite the expression), it means that the power that drives the speaker is such that the voltage aspect of the power is constant regardless of the load. (Voltage is an aspect of power just as current is; 1 watt equals 1 volts times 1 amp.)
IOW such an amplifier is termed a ’voltage source’.
The thing is, an amplifier **DOES NOT** have to double power as impedance is halved in order to act as a voltage source!!
Tube amplifiers can behave as voltage sources (after all, the this idea was originated by MacIntosh and ElectroVoice back in the 1950s) and they certainly don’t ’double down’... But they **can** cut their power in half as impedance is *doubled* and that is how they manage being a voltage source. The thing is a solid state amp does that as well. Its only at **Full Power** where 'doubling down' might make a difference and right after that is clipping, so its not that big of a deal since the amp really should not be running anywhere near full power if its a good match with the speaker.
So in a nutshell the ability of an amplifier to double power as impedance is halved is not what makes for a good sounding amp, and it may not be important at all; certainly with most speakers on the market its not. In fact the number of speakers that have horrendous amplifier-torturing load impedances (and phase angles) is actually pretty limited. Its a simple fact that the harder you make an amplifier work, the more distortion it makes so its unlikely that a speaker that is horrible to drive is going to sound like real music regardless of the amplifier employed.
So the whole thing is a bit of red herring.