The best of both worlds would be a speaker with separate inputs for each driver and a passive crossover that could be easily toggled with a switch. You could use a single amp to drive it like a regular passive speaker or separately amplify each driver.
Honestly, I would prefer that speakers came with the inputs to independently drive each driver and dropped the crossover entirely. It would have the advantages of active designs while still letting you choose the electronics. Active crossovers are better these days, and there's no sense spending money on a complex passive crossover that you're not going to use.
We would just need better options for low power amplification. In such a system one would need something like 50W x 8 instead of 200W x 2.
From what I've seen, speaker driver efficiencies follow this trend:
Subwoofers often have the lowest efficiency, in order to keep the required box size down.
Midranges and fullranges often have the next lowest efficiency, though you can certainly find examples of high efficiency midranges.
Woofers come next.
Tweeters as a group probably have the highest efficiency.
On the other hand, the spectrum for music is typically quite tilted. The means you need more power at low frequencies in general, though the increase may flatten off somewhere around 100 Hz.
What this means is that a rather typical consumer may need 500 watts for their subwoofer (use a separate amp here, it makes total sense). Then they need 200 watts for their woofer, 50 watts for their mid, and 15 watts for their tweeter (unless they want to pass test signals with flat spectrums correctly). The issue here is that once you need that 200 watts for your woofer, if the technology is perfectly capable of simultaneously providing the 50 watts for the mid and the 15 watts for the tweeter, then using separate amps just adds to the expense without any real gain.
As for the topic of the larger thread:
Regarding DSP, it's been mentioned that adding delay to align acoustic centers only works for one spot. With dispersion in mind, it's not typically a good idea to have wildly different acoustic centers. Passive crossovers can be used very effectively to combine drivers that aren't too far separated in distance, although variations from theoretical slopes will be made. There's nothing magical about text-book slopes anyway, so deviating does not degrade the sound.
Phase can be manipulated with DSP, but a speaker doesn't have to be active to do it. Additionally, typical speaker phase distortions above 1000 Hz are completely inconsequential. The same is true below 200 Hz where the room dominates. There's probably some small frequency range between 200 Hz and 1000 Hz where phase distortion could even be perceived by most people (listening to speakers in a room), and then there wouldn't be a strong preference for distortionless playback. Phase correction is just not very important to human perception of sound... it can be more important for marketing with pretty graphs, though.
Passive crossovers sometimes have to attenuate a speaker driver to match other less sensitive drivers in the speaker. This wasted energy could be conserved with an active speaker. On the other hand, if you're using more amps, they have a certain draw all the time. I don't think this is a big deal either way.
DSP can also make the frequency response flatter in magnitude. However, there's a point where this also becomes inconsequential. Is a speaker that's +/- 1 dB from the target response perceived as better than a speaker that's +/- 2 dB? How about 3 dB? There are plenty of passive designs that are within +/- 3 dB (or less) from their target.
As an amateur speaker designer with a degree in electrical engineering, and a couple decades of DSP experience... I design passive speakers. Even my multi-way line arrays with very narrow and consistent beamwidth are passive. I could have designed them to use DSP, but I figured it was in my best interest to check first whether a passive implementation was possible. It took me a few months to figure out how to do it for one particular design, and then a few more months to generalize it, but it's possible. They are efficient enough that I honestly run them off an AVR. A nice, cheap, mass produced AVR.