The flaw in that logic is that with bi-wiring, the signal travelling down each cable is identical. This is also true of passive bi-amping. The only way to make it so that different signals travel down each speaker cable is with an active system using an external electronic crossover to split the signal into a low frequency range and a high frequency range. These must of course be amplified by two seperate amplifiers. This is active bi-amping.

The only thing you "replace" with bi-wiring is that jumper that resides on the back of your speaker that shorts the two inputs to the passive crossover - the frequency split is done inside the speaker by this crossover network.

With bi-wiring, you are only moving that "jumper" from the back of the speaker system to the output terminals of the power amplifier - there is no electrical difference other than the effective gauge of the speaker cable is doubled. The same electrical result can be had by using a single run of larger gauge speaker cable.

At least with passive bi-amping the amplifier used for the high frequency section does not have to supply current in the low frequency range. An argument could at least be made for the benefit of this, although the audible benefit is questionalbe. This arrangement is also wasteful of resources, especially for the high frequency section.