The simplest electrical crossover on a speaker is an inductor placed in series to the woofer, and a capacitor to the tweeter. The amplifier drives into both simultaneously. If they are perfectly equal and opposite in "reactance", then they cancel out, as far as the amplifier is concerned. This cancellation is what makes this the only dividing network without time-delay distortion.
This is a first-order network. Its two components can be used only when the drivers and cabinet designs are "perfect".
Not bloody likely.
More complex circuits are usually required, whether using two or ten more parts. The result can still be a "measured" first-order acoustic rolloff. The extra parts "modify" driver non-linearities and "make up" for cabinet reflections. Which they cannot- but they can fool the microphone. Of course, extra circuit-parts cannot be perfect either. Reductions in transparency and dynamics are givens.
To keep the number of crossover parts to the barest minimum, one has to use the most linear drivers- which are relatively few. However, not that few: specific examples include tweeters from Morel, Dynaudio, Foster, Stage Accompany, Pioneer TAD, and Scanspeak. Certain mids from Audax, Eton, Davis Acoustics, Bandor, Jordan, Foster, Peerless and Aurasound. Specific woofers from Scanspeak, Davis, PHL Audio, Volt, Audax, Peerless, Pioneer and Aurasound. There are others.
And every one of them is far more expensive than the drivers used in most designs.
For a commercial designer who wants to use the simplest crossover, it's hard to find the best drivers under deadline conditions. But by using the most linear drivers, within proper cabinetwork and correct bandwidths, the crossover circuit can be reduced to just a handful of parts, for clarity and for time coherence. The converse is entirely true.
Best,
Roy