Analog active crossovers work just like digital ones, high and low pass filters before the amplifiers.
Each set of drivers get its own amplifier so amps see a resistive load.
This approach virtually eliminates IM distortion which is what your ears dislike most.
Passive speaker crossovers are eliminated, no phase shift, added resistances or unwanted delay. Just not all the bells and whistles of a DSP, thus no digital "noise".