@atmasphere’s post reminds us of why electronically separating a woofer from the midrange/tweeter drivers can provide better sound; bi-amping, with an outboard x/o over dividing the signal before the two power amps, one amp for the woofer, the other for the m/t. Done so, nothing the woofer does (amplifier power supply demands, back-emf, etc.) effects the m/t drivers, the same with the woofers’ amp.
A side benefit of this arrangement is that the component values used in outboard x/o’s are generally of much lower value than those in speaker-level x/o’s. Line-level components are much cheaper and smaller than speaker-level ones, and can have less of a sonic signature.
Then there is the matter of the physical vibrations created by woofers. With the woofer removed from the structure housing the midrange and tweeter drivers, the m/t are free of the structurally-transmitted woofer vibrations, a good thing. And, with the woofer in its’ own enclosure, if the x/o frequency is low enough that enclosure can be located so as to optimize the woofers' performance, the m/t drivers to optimize theirs’.