I second Stan's comments. You need to keep the low frequencies out of the tweeters, or you will destroy them. You need to keep the high frequencies out of the woofers, or (at best) you'll mess up the frequency response in the crossover region. Tone controls on the integrated amps are unlikely to accomplish these things adequately. And at best you'll wind up with a very crude approximation of what the speaker designer intended his crossover network to accomplish, which will undoubtedly sound poor. There is also the practical issue of having two separate volume controls, as Stan mentioned.
Finally, to the extent that low frequencies are not kept out of the power amplifier section of the integrated amp that feeds the tweeters, using a more powerful amp on the woofers will be pointless. How loud you can turn up the volume will be limited by the clipping point of the lower powered amp, if the lower powered amp is allowed to see most or all of the bass content of the signal.
Oftentimes simpler is better!