A technically good amplifier is like an ideal voltage source with a low output series resistance and able to supply whatever current a load (wire, crossover, drivers) require. The problem is that the long wire presents a series resistance and inductive load with some shunting capacitance which causes the signal at the loudspeaker end to be different from that at the amplifier end, depending on the current being drawn. Even this is a gross simplification. Engineers model elements of a system to be good enough. Enough for what? Enough for realization of basic function and requirements. This doesn't mean that a power amp with a DC supply that can deliver 5A at 50V is perfect even though that supply meets its' specifications. In your computer chip, to ensure that a logic gate triggers when expected. As those systems get smaller and faster, the models have become more and more sophisticated to satisfy basic functional needs.
Separating the upper and lower sections of the loudspeaker crossover from each other (requires separate terminals) will allow parallel runs from the amp to the speaker. The most basic factor is that, all things being equal two sets of cables will halve the series contribution of the wire to the system signal disturbance. This can also be achieved with a shorter run of wire.
The bi-wire improvement will mostly come about because the high current woofer load distortions will no longer generate a voltage disturbance signal at the tweeter since they will not be present at the high terminals or at the amp terminals (assuming the amp is not a tube type with high output impedence). I could beat this to death but a simple circuit analysis using non-ideal elements will show this. So much for the assertion that there is no science, or more accurately, technical basis. Many people learn basic I=E/R and think they understand everything. A loudspeaker is not a simple 8 ohm resistor, a cable is not equivalent to a small resistance, and I=E/R are not frequency independent.
Years ago, I used to argue vehemently, as an arrogant, self-assured electrical engineer, that power cords couldn't make a difference because the amp converted (rectified and filtered) AC into DC. My model must have been too simple since after finally trying different power cords and conditioners my reaction was: "No freaking way!". I've since come to see that the amount of benefit of a power cord depends on the application. I've found the biggest improvements with high power class A amps which are always generating large current pulses, and for relatively noisy components like DACs etc. My preamp was not very sensitive to the power cord since it utilized a sophisticated DC bus followed by a 400 Hz AC system which was then reconverted to DC.
