This way (i.e.: both getting rid of the passive crossover on the output side of the amp and having each amp channel drive a limited frequency span) the individual amp channels will see a significantly easier load presented to them, thereby making more effective use of their power envelope and quality potential; finally control the drivers better with direct driver connection and harnessing more of their potential as well.
@phusis
I do agree with this approach. In addition to the benefits you cited, you can match amplification with frequency range; for instance, those old Bryston monoblocks you have laying around will do great on bass duty, leaving you free to spec SS Class A amps on mids, etc. or as your heart desires.
Active crossover implementation is far from trivial, though, especially if you wish to avoid the AD - DA conversions a digital crossover entails.
You could put together relatively inexpensively active speakers with onboard modular amplification and a USB-programmable DSP module or even a SBC running Linux. Thermal management is going to be tricky if electronics are integrated onboard the speakers. I've been kind of mulling over something like that.