With the jumpers removed on a bi-amp capable speaker, the impedance of each section is not the usual 4 or 8 ohms, but several hundred if not more at the frequencies that the amp is "not supposed to be amplifying". Higher impedance means less current draw. No meaningful amount of current, no wasted power.
According to a recurring audio-myth, only an active crossover should be used for biamping, in order to split the band before the power amp instead of inside the speaker, thereby reducing the amount of work each amp channel has to do. While active crossovers do have their place in PA systems, it should be noted that equalizers are also a part of it.
A generic active crossover on its own merely divides the audio band into smaller ones. The carefully custom-designed crossover in a high performance home audio speaker does a lot more. It is responsible for correcting frequency response aberrations of the individual drivers, maintaining phase coherence between drivers, optimizing off-axis response, balancing levels between drivers, setting up impedance, at times improving woofer performance by rolling off not just the top, but also frequencies that are too low and cause it to misbehave, and other things that vary according to model.
Tearing out the speaker's own finely-tuned crossover to replace it with an active crossover with generic controls almost guarantees that, just for starters, frequency response will be altered. Different sound doesn't mean a better sound. Using the passive crossover in the speaker is indeed the correct way to bi-amp.
(What's bi-amping? It's using one amp channel for the speaker's mid-high frequency drivers, and another for the low-frequency drivers. The speakers must have separate inputs for this - be sure to remove the jumpers from the speaker inputs first or amp will become instant toast! If one amp starts running out of power, usually the one driving the woofer, then the other side remains clean instead of becoming part of the problem, a double-win. This is the very idea behind bass management and powered subwoofers in home theater systems.)