Perhaps I'm not understanding what you're saying. I'm reading this as you are contending that not only is the voltage the same on both amplifier outputs in a passive bi-amp pair, but the current is the same too. So, to extend the thought, a 40Hz signal will be delivered to the midrange-tweeter section of the crossover at the same current level as it is to the woofer section of the crossover. Does that mean you think the 40Hz current delivered to the midrange-tweeter section is dissipated as heat in the crossover components?
Nope, the opposite, never said current is the same, unless I made a typo somewhere. It depends upon the frequency distribution and impedance over frequency. I used an example of both treble and bass being 8 ohms as an illustration of how load impedance might not change since the OP insists that it is "more" when you bi-amp. The speaker's impedance does not change when you passively bi-amp though is split into two parts.
Couple of examples follow (I did not look up their crossover frequencies).
B&W 702 has low impedance spots at high and low frequencies:
ML Montis has its lowest impedance in the HF region:
Power distribution is frequency dependent so power, and current, will change even if voltage does not. Most audio amplifiers are designed as voltage sources and so if the voltage clips in one amp it will clip in all in the AVR passive bi-amping scenario. In fact there will be a bit of headroom improvement if power is significantly different due to less drop across the output transistors, but that is typically very small (<1 dB) IME. And that is only at or near clipping. But as was noted above, Amir has found some amps that clip "poorly", but I suspect those are outliers. In any event, if you
are clipping, chances are you need more like 3~6 dB of additional headroom and thus 2 to 4 times the power.
Two things are getting conflated that I was trying to explain (obviously poorly): impedance is not necessarily "more" when you bi-amp, and power delivery depends upon impedance and the frequency content in the source. The usual argument about frequencies is that treble takes much less power than bass. That is not always true, either -- depends upon where the crossover is for the speakers, and perhaps even less so for systems that have subwoofers and thus offload the deepest bass.
It is correct that Class A & AB amplifier output stages have a standing bias (and it can be considerable in some designs), so powering four Class AB amplifiers in place of two will consume more power just sitting there idling. With the Class D amplifiers in many receivers I'm not sure how significant this factor is. (I suspect it is insignificant, but I don't know for sure.)
Yes, I agree, I do have some experience with various amplifier topologies though limited in audio. Class D's efficiency is also worst at low output. The quiescent current is usually lower, sometimes much lower, than for class A or AB amplifiers but is not zero and thus using four amps, even class D amps, will use more power than two amps for the same total output power. I believe that is all I said (made no attempt to quantify it; I have seen numbers from maybe 1 to 10 W but not something I track). For class D in AVRs implementing "passive" bi-amping it is worse because the amplifiers are are swinging (and slewing) full voltage even if there is less power delivered to the load. Of course, they are more efficient, but the net power still goes up. A truly bi-amplified system, using active or passive line-level crossovers before the power amps, is more likely to provide additional headroom (voltage and current), but even that is not guaranteed. Again depends on the relative frequency distribution and impedance of the speaker over frequency.
IME/IMO - Don