Why aren't component active XOs more popular?

Sean and b.l.z: There is a very clear distinction between active amplifier and passive LCR networks.
First, the active circuit has much more non-linearity than the passive network, leading to different types of distortion. You get more mixing (IM distortion) with active components, and those are not directly related to the originating tones.
Secondly, most analog active crossovers are implemented with high-gain opamps, which means that the designer had to apply high-levels of feedback in order to achieve low gains (usually unity at the passband). There is a specific sonic signature to that type of circuit. Cheap implementations may have slow loop delay so the delay-induced distortion may be very crude. The high-speed opamps are better in that regard, but still - "no free lunch"...
Digital crossovers have digital issues and analog issues. Cheap implementations have all the "good" traits of digital audio, in terms of converter non-linearity, clock jitter and sometimes crosstalk of digital into the analog circuitry, which raises the noise floor. Just listen at high gain to low level passages, where the noise floor is most apparent.
Bottom line is: there are issues...
Of course passive crossovers are not a magic solution, but they may be the least of all evil. If the drivers are well matched (some brands modify drivers or develop their own) then the passive crossover can be simple and accurate.
Last thing to add about multi-amping. Splitting audio signals is a nasty thing to do. It's true that a multi-driver speaker does that too, but in that case it's a necessity, unless you accept the limitations of a single-driver speaker system. I believe most people don't.
With the passive approach we assume that the speaker designer has done a decent job and the response would be acceptable with most commercial amps. That's not always true, but at least there is a good chance this will happen.
With multi-amping, we not only split but also run different amps and cables for each "band". Each path is a different audio chain, with differences by design (like solid-state for bass and tubes for mids and treble) or due to production tollerances. So not only do you have to measure drivers and match the crossover, but you also have to consider the full chain.
It's all doable. In fact, with digital crossovers it can be measured and the filters re-calculated in real-time, like some systems adjust equalization for room modes. It's a convenient way to do things, if everything can be matched and the above issues resolved.
Don't misunderstand me. I'll agree that for some price points the active approach is a good solution. I'm not sure that's true for achieving the ultimate sound. All this is my own very subjective take on amplification.

Serus: As mentioned, my Brother went from using a 6 dB per octave passive crossover using very high grade parts in a passively crossed multi-amped system to an "antique" active crossover that was used professionally and beaten to death. After hearing the difference for himself, he pulled all of the passive parts and bought an active crossover. Bare in mind that his initial testing was done just listening to a tweeter with a cap in series vs the tweeter actively crossed at 6 dB's. Not only were the differences HIGHLY audible using even a "low grade" active crossover, there are measurable differences in amplifier performance and efficiency involved in such a situation too.

Factor in that most dynamic tweeters are far less demanding of a load on an amp as compared to a large dynamic woofer and the benefits would have been even more apparent at low frequencies.

You have to remember that the passive crossover is dealing a high level signal from the amp and the reflected EMF of the drivers simultaneously. When you use an active crossover, the efficiency of the amplifier is markedly increased due to the reduction in bandwidth. That is, the amp is no longer trying to reproduce power that ends up getting "wasted" in a passive multi-amp system. The end result is that transient response is improved, distortion is lowered, thermal stress is reduced, etc... Speed and clarity is improved in every respect. The fact that the active crossover is dealing with miniscule amounts of line level voltage whereas the passive crossover circuitry is dealing with both much higher levels of voltage and current should explain why the whole system sounds "more stressed" once those parts are introduced into the equation.

On top of that, the amp doesn't see the added reactance and phase shifts of the passive circuitry as part of the load as the amp is now in "direct drive" mode. That is, the amp sees the nominal impedance of the speaker cable and the electrical characteristics of the driver itself. As such, it is a "purer" load for the amp on top of the added benefits of active bandwidth limiting mentioned above.

Granted, some specific amp / speaker combos may sound better with a passive crossover, but that is typically because the amp itself isn't up to the job at hand. Then again, getting rid of all of the other "garbage" between the amp and the drivers themselves can also be the difference between an "inadequate" amplifier and a "good" amplifier in such a system for the aforementioned reasons. It can be a tough situation, but as mentioned elsewhere, if the drivers are good units and well-matched to begin with, anything other than an active system will degrade the sonic potential of an otherwise excellent set of speakers. Don't believe me? Try inserting a cap in series with your tweeter and see for yourself. Sean
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I am using an active crossover for my InnerSound EROS MKII
speakers and I like it bunches.

Who says they aren't popular? The reason you don't see many is once you have one in your system--You are not going to give it up! Occassionaly you will see one and they sell fast. For me the greatest single improvement was going from a passive bi-amp system to an electronically XO system. There are some caveats: With 3-way electronically XO's, (ie tweeter, mid & bass), there is a much higher probability of blowing tweeters (in my 3-way system I have blown 2 sets of tweeters in the last 5 years--and both times I did something stupid); then there's the hassle of 3 amps and the clutter of that much more cables and wires. But the sound makes it worth it IMHO. Marchand has wonderful kits for electronic XO's. You do have to set levels but this also gives you the flexibility to make it sound the way YOU like it. The other beautiful thing, is it frees up your tube amp to do the things they do best and allows you to use a solid state amp to do the grunt work of bass. And one more thing: If you are building your own speakers, designing a passive cross-over is extremely difficult. You can buy software or have someone do it for you (recommended if you must go passive) but by the time you buy first rate components, you probably could have bought an electronic XO and I think the electronic XO will sound better!

Again, I remind people that a major advantage of electronic crossovers is to reduce the power amplifier power requirement, and to avoid IM distortion. Both of these advantages have become less important with the advent of solid state power amps. For those who still use tube power amps, tube crossovers are available (for example from Marchand).

With old style tube amps the improvement with an electronic crossover is dramatic. With modern solid state amps the improvement is less, being related only to avoiding the problems of the passive crossover.