This argument seems kind of silly. As with class A and class A/B, a class D amp's output power at any given load impedance is limited by its voltage and current capabilities.
In class A and class A/B amps, the output transistors are dissipating power proportional to the bias current and voltage across them. Most class A amps (although not all) are set up with enough bias to operate in class A only into 8 ohms, switching to class A/B into lower impedance loads. With adequate heat sinking (and a big enough power supply), their thermal capabilities can generally support enough current to double power into 4 ohms and again into 2 ohms (and some even again into 1 ohm), since the voltage across the output transistors carrying the current is lower when they are delivering the maximum current.
This is where EPDR comes into play, because if the phase angle requires high current while the output voltage is still low, the thermal limits of the amp can be quickly exceeded.
Class D amps operate differently, since the transistors are almost always either in saturation (where maximum current is flowing, but with very little voltage across them) or turned off (where no current is flowing). The only time they are dissipating significant power is when they are switching from on to off or back (this is obviously a simplification). but this is a small percentage of the time. This is how class D amps can be so efficient.
But there is nothing about class D amps that would prevent you from building an amp that doubled power as you halved impedance. It's just that there is not the same benefits to do this as their might be in a class A or A/B amp. The amp is not going to run much more efficiently at half the rail voltage like a linear amplifier will.
Since most speakers are nominally 8 ohms (or slightly less), most class D amplifier designs are optimized for this load. But that doesn't mean you couldn't build amp to do what you're describing. The Hypex and Purifi modules, for example, can be operated at a lower voltage with the same high-current power supplies to create an amp that can easily achieve what you are talking about.
If you ran a Purifi module at around 35v, it would be limited to about 30w into 8 ohms, 60w into 4 ohms, 120w into 2 ohms, and could probably achieve 240w into 1 ohm. But why would you want to do this since you could achieve almost the same power into 1ohm and get over 200w into 8 ohms without generating much heat by using a higher voltage supply.
In class A and class A/B amps, the output transistors are dissipating power proportional to the bias current and voltage across them. Most class A amps (although not all) are set up with enough bias to operate in class A only into 8 ohms, switching to class A/B into lower impedance loads. With adequate heat sinking (and a big enough power supply), their thermal capabilities can generally support enough current to double power into 4 ohms and again into 2 ohms (and some even again into 1 ohm), since the voltage across the output transistors carrying the current is lower when they are delivering the maximum current.
This is where EPDR comes into play, because if the phase angle requires high current while the output voltage is still low, the thermal limits of the amp can be quickly exceeded.
Class D amps operate differently, since the transistors are almost always either in saturation (where maximum current is flowing, but with very little voltage across them) or turned off (where no current is flowing). The only time they are dissipating significant power is when they are switching from on to off or back (this is obviously a simplification). but this is a small percentage of the time. This is how class D amps can be so efficient.
But there is nothing about class D amps that would prevent you from building an amp that doubled power as you halved impedance. It's just that there is not the same benefits to do this as their might be in a class A or A/B amp. The amp is not going to run much more efficiently at half the rail voltage like a linear amplifier will.
Since most speakers are nominally 8 ohms (or slightly less), most class D amplifier designs are optimized for this load. But that doesn't mean you couldn't build amp to do what you're describing. The Hypex and Purifi modules, for example, can be operated at a lower voltage with the same high-current power supplies to create an amp that can easily achieve what you are talking about.
If you ran a Purifi module at around 35v, it would be limited to about 30w into 8 ohms, 60w into 4 ohms, 120w into 2 ohms, and could probably achieve 240w into 1 ohm. But why would you want to do this since you could achieve almost the same power into 1ohm and get over 200w into 8 ohms without generating much heat by using a higher voltage supply.