Hmmm, I would have said it differently. With bi-amping you get twice the power (assuming equal amplifiers), theoretically resulting in 3db of additional loudness in the audible frequencies, at a cost of extra channels of amplification, extra electricity, extra interconnects (or a y-splitter), and twice the speaker cable.
Since the average input power to most speakers is less than 4 watts, and often less than 2 watts, I wouldn't worry much about heating up the crossover.
Whether or not bi-amping is an audible benefit seems to depend on some pretty subtle variables. For example, some speakers present rather punishing loads in some frequency ranges but not others. My old Legacy Audio Focus were like that, since it seemed like the designer just hooked three 8-ohm woofers in parallel for the lowest three octaves. (I know he probably didn't, but looking at the measured impedance curve for that speaker one might think he did...) Some people also like to convince themselves that multi-driver woofer arrays generate a lot of back-EMF that negatively affects the amp, or that arrays of mid-range drivers and tweeters complicate loads, and that separating these arrays from the woofer arrays through a passive crossover somehow improves the sound. I have no idea if it does, but my gut feel would be that it mostly doesn't, for amps that perform well into both high-impedance and low-impedance loads. With some speakers with complex driver configurations and lower power amps you might get better sound with bi-amping, but when I see folks that want to vertically bi-amp a two-way, two-driver speaker using 200w/ch amps, well, I just have to shake my head.
One other thought, your ears work logarithmically, but your sense of touch doesn't. A 3db increase in power causes a small increase in loudness at 40Hz, but you feel about twice the slam, because it's twice the delivered power.
Bi-wiring looks to be a complete waste of money if you use wires of the proper gauge. The audibility of bi-wiring must be one of the biggest lies in the audio world.