Bi-amping vs Passive Setup

That's not exactly how it works.  It's not resistors that provide the filtering but capacitors and inductors (with help from resistors).  The impedance goes to infinity in the "unwanted" frequencies, and the current drops to near zero.

When you bi-amp and don't use an active crossover the amps will still produce full voltage swing of all signals, but no longer have to provide full current, so you are getting more power supply per speaker. 

If you'd like more insight into how crossovers work in this particular case I wrote something up here. 

There are a lot of variables in play, so the approach differs depending on them. One size does not fit all.  Bi-amping can be simple or complex - vertical, horizontal, passive, active, or hybrid of several approaches.  Are the speakers 2-way, 3-way, or other?  Where are the crossover points?  What impedance will each amp see? How many amps will be used? (etc)

I use a combination of tube amps with an inline high pass filter at 60hz to drive the midbass and tweeter that have a passive crossover of top notch parts, along with an active low pass crossover that feeds a solid state amp to drive the woofers and also feeds an active subwoofer.  It started simple, and the configuration has evolved over time. 

Every system and situation is unique, so really needs to be addressed as such.  There are benefits and challenges, but I’d encourage anyone to research a d bit, and explore it.  There are many ways you can go, so don’t let anyone tell you there’s only one "true way" to bi-amp.