But, of course, this isn’t the case. Typical class D amps are 90% or more efficient into 8 ohms (at max output power), but efficiency drops by approximately 40% into 4 ohms, and 40% again at 2 ohms.
I am not sure you wrote this correctly. I think you mean losses go up 40%, or stated as efficiency, the reduction in efficiency goes up by 40%, i.e. 10% reduction becomes 14%?
Conduction losses are I^2 * R. At the same wattage, half the resistance, current goes up sqrt(2) = 41.4%, so losses must go up 100% due to conduction losses, but realistically total losses are going to be a quiescent component (in this case about 11 watts), plus a linear component and a squared component to come up with a very good model.
For reference as example, the NCORE 500 OEM module is about 95.2% efficient at 400W/8 ohms, about 92.6% efficiency at 400W/4 ohms, but drops down to about 87.5% at 400W/2 ohms. Losses are 20, 32, and 67 watts at 8/4/2 ohms, 400W output.
For the NC500, the current limit is 26A. That puts maximum possible RMS power at 2ohms = (26/sqrt(2))^2 * 2 = (26*26/2)*2 = 676W, not too far from the rated power of 550W as a ratio, and even closer if you add losses above to the 550W.