That is correct. The rail voltage of the avr-x4400, x4500H are >60 Vrms so I don't consider it volltage limited, but current limited, most likely same for the x4700, x4800h.But "7.07*7.07*8 = 400 W into 8 ohms" would only be achievable if the maximum output voltage from your simplified numerical example were doubled (i.e. 56.56 V).
As I said, it would have been better if manufacturers would include their voltage and current limit, instead of power. But they won't do that, nor would they tell us the power transformer VA rating. Some separate power amps manufacturers do, such as Parasound, but they typically did it in a wishy washy way. Most, such as Emotiva, Anthem, would just describe their transformers "huge", without the VA, V, I, "huge" is subjective lol...