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.