Speakers have "crossovers" - low pass and high pass filters to split the incoming signal to the woofer and tweeter. High quality filters that can cope with the power levels found in speakers are expensive and difficult to build, so most manufacturers opt for very simple designs that look like they started off life as part of a washing machine (have a look at one on the web, they look like Dr Frankenstein designed them). These filters make life difficult for the amp, as they can introduce all sorts of kinks and bumps into the impedance curve - the load that the amp "sees" at different frequencies.
A far, far better solution is to split the signal prior to amplication and have one amp per speaker driver. The high and low pass filters before the amps only have to work at line level, and it is much easier to build high quality electronic filters with components you can solder to a circuit board as opposed to components you have to bolt together in a speaker enclosure.
An even better solution is to use DSP - digital signal processing. Instead of using electronics for the filters before the amps, highly sophisticated filters can be implemented in software - not just crossing over between the two speaker drivers, but correcting for speaker cabinet resonances, speaker driver non linearity, and phase mismatch between the drivers.
Put all the bits (DSP processor, dacs, power amps) in the same box as the speaker and you have a digital active speaker. Make the DSP system programmable with a link, and you could customise the performance of the speaker to the room it was being used in.
Sound like science fiction? This is how pro audio systems are now, in recording studios and in particular, large venue flying arrays that are tuned and "steered" using these techniques.
Some consumer hifi manufacturers do use these techniques, the Sonos play 1 is a good recent example, and at the high end of consumer hifi Boothroyd Stuart and Meridian have set the pace. A good primer is a white paper written by Caleb Crome who was responsible for the Squeezebox Boom. Google it and it is well worth a read.
An interesting question is if the pro market has pretty much converted to active, and if Logitech could fit a wireless card, an Ethernet system, a DSP processor, 4 speakers, 6 dacs and 6 power amps (2 were used for headphones) into a squeezebox boom for less than £200, then why is the consumer hifi market still messing around with passive speakers?
A good question indeed.