For the most accuracy you need your sub-woofer configured such that its sound sums flat with the main speakers at your seating location (this requires the appropriate magnitude and phase relationship)
For the most accuracy from any speaker you need it placed so that you're not getting cancellations from the reflected waves as the difference between direct and reflected sound approaches a 180 degree phase shift (282 feet to the point of reflection/ frequency) and so that the bass/midrange increase you get as it couples to the wall behind it is addressed with its cross-over baffle step compensation.
For the most accuracy from a system you need to avoid pushing drivers high enough that they break up or beam, or low enough that the distortion that goes with excursion is not too high.
The type of music, playback level, etc. may change which distortions are less objectionable but can't change physics.
Transfer functions are all that matters whether they result from acoustic or electrical effects.
An analog low-pass or high-pass filter or digital filter that acts the same (Signal processing is outside my area of engineering) has an inherent phase shift. The outputs from high and low pass filters of the same type and order put the outputs 90 degrees out of phase for each order.
The highest bass accuracy also results when you don't put energy into a room below (565 feet / longest dimension) Hz.
All this explains why big speakers don't work well in small rooms and what sub-woofer/main configurations produce the flattest (or most enjoyable with a given type of music) response.
If you have a sealed speaker its mechanics mean you have a 2nd order roll off. You get it and the woofer to sum flat with a 2nd order electrical low-pass on the sub that inverts its signal, the F3 points match between speaker and cross-over, and both share the same Q. This is why sealed speakers mate well with something like an REL that has a cross-over with adjustable frequency and Q.
The attenuation and phase shift an octave into a system's pass-band are negligible. You can high-pass a set of speakers an octave above their F3 point and low-pass your sub at the same frequency. They'll sum flat with a fourth order electrical cross-over. Or a second order electrical with the sub inverted. This is why fourth order cross-overs an octave above the speaker's F3 point work well.
In a sealed speaker excursion doubles for each octave lower (halving of frequency) you go. Once a ported speaker starts rolling off its excursion quadruples with each octave drop. Distortion comes from excursion, so distortion increases faster in ported speakers below their cross-over point. A 4th order cross-over maintains constant excursion on the speaker so excursion isn't increasing. This is why a higher order cross-over works better with ported speakers.
When you pair a sealed speaker with a second order high-pass and sub with fourth order low-pass you can get them to sum flat. THX home theater systems do this with sealed speakers having poles at 80H Q=.707, a second order butterworth electrical high-pass, and fourth order Linkwitz Riley low-pass. You have an LR4 response on both.
When you get a 1/2 wavelength length difference (say 3.5' from a wall for 80Hz) you get cancelations. With a speaker 4' out you don't have cancelation above 80Hz. With the sub-woofer in a corner you don't get a cancelation at any frequency. By the time frequency drops enough for a speaker to couple to the wall behind it it has little output. The sub-woofer is always operating in the same space so it is unaffected by this. This is why softit or in-wall speakers can work very well.
A higher order sub-woofer low pass keeps its cone out of breakup.
Etc.