Except you're forgetting what happens in the speaker with the passive crossover network. When one amp is driving the full "system" inside the speaker all frequency ranges are going to some driver with an impedance with allows for easy current flow. But when you remove the straps; you separate the system into a high-frequency range with a high-pass filter, and a low-frequency range with a low-pass filter. The other half of those ranges basically end up seeing a very high impedance, and turning the amp's energy to heat.
So when driving the speaker system 100 Watts, across the range, drives some part of the speaker's full system. When bi-amping, 100 Watts drives the highs, and 100 Watts, drives the lows. You're still only getting 100 Watts to any part of the speaker.
If you were to use the pre-outs on a receiver, input them into an active crossover network, remove the crossovers components from the inside of the speaker (make sure your active network matches the passive parts in point and slope), then get separate amps, with fine grained gain control, along with a precise audio spectrum analyzer to balance the gain of each amp against the driver it is feeding for a flat response. You might get some benefit from bi-amping.
The bi-amping built into receivers, feeding a passive crossover network, is an entirely marketing based feature; one manufacturer offered it, so they all have to offer it.
EDIT: Oh, I forgot to add. In the presented scenario, with one PS providing power to multiple channels, when bi-amping, you're more likely to exhaust all that's available because you have two channels with exactly the same content being driven to the same levels, but half of it being used to make heat instead of sound. The way multi-channels amps get away with higher single channel ratings, is that in the real world it isn't common for more than a stereo pair of channels to be driven hard at one time in anything other than test signals. But with bi-amping you quickly run into cases with 4 channels being driven hard.
Chris- I (mostly) agree about only having 100 watts available to any part of the speaker system. What I was thinking, but didn't say clearly, was that if you bi-amp (passively) the speaker you unload each amp from having to drive all speakers. For example, if a signal has 90 watts of 100 Hz content and 10 watts of 10,000 Hz content for a total of 100 watts a single channel/amp has to drive that total power. But if you separate the highs from the lows than the tweeter amp is only driving 10 watts. The 90 watts of low frequency power on that amp sees the very high impedance of the HPF so is delivering only very low power at that frequency. Related to that, I don't really understand your statements about the crossovers dissipating lots of heat. If you define the crossover as just the reactive components (inductors and capacitors), then the only heat generated is due to the resistive and parasitic losses in those components, which is very low for high quality parts. The high impedance of the HPF at low frequencies and the LPF at high frequencies presents a high impedance load to the amp, so very little power goes to that section. (It's true that the resistive elements, which aren't really crossover but are for gain balancing, etc. do dissipate power, but that is equally true whether or not the speaker is bi-amped.) Of course, as you said, using an electronic crossover ahead of the amps allows all equalization and gain matching to be done without any passive components, so no losses.
