Adding subwoofer to Full-Ragne Speakers question

Me no electrical engineer either, but think of it this way -- folks bi-amp speakers, right? And the point is both to increase the power to each individual set of drivers and to put correspondingly less demand on each amplifier in order (which is why folks presumably do it) to improve the sound. Depending on how, where in the signal path (and if) you've got a crossover dividing things up, the addition of a powered sub could work in exactly the same manner. As long as there is some sort of crossover in the chain before the signal gets to the speakers, the speakers should never see the low frequency demand (nor place the power requirement demand on the amp in order to reproduce it) as those low frequencies would be sent to the sub (with its own, private amplifier). The functional equivalent of bi-amping by proxy. Thing is, while they could be, I bet most subs simply aren't set up this way (which is only right an proper, when you're talking about a full range speaker in the first place). Rather, they are simply put on top of the existing setup: the amp and the speakers continue doing exactly what they were doing before the sub got there and the sub just provides "extra," instead of redistributing the signal, or power demands or responsibility for makeing certain sounds. Sure, this might make "everything" sound better for a whole number of reasons, real or imagined, I just have a lot more trouble coming up with a rational, electrical explanation for the improvement in the second scenario.