The omnidirectionality of low-frequency wave radiation is not a sufficient condition for proper interaction of the subwoofer with the main speakers. The assumption of omnidirectional radiation is already met in the range of approximately 300 Hz, but the operation of the subwoofer-satellite system with the crossover frequency in this range is weak, and the acoustic integration of individual ranges is not proper.
This problem results from the phase relationships between individual loudspeakers that cooperate in processing the entire acoustic band. In a loudspeaker assembly, the loudspeakers operate in a specific electrical and mechanical configuration so that they radiate in phase in the crossover frequency ranges. The wavelength of the 300Hz wave is about 115 cm, which is much longer than the diameter of the diaphragm of even a very large woofer (hence the condition of spherical wave radiation is met), but 1/2 of this wave is only about 58 cm, and at such a distance there is a shift phases by 180º. This means that at a crossover frequency of 300Hz, moving the subwoofer forward or backward, relative to the satellite speakers and the listener, causes a phase shift of 180º within the range where both parts of the system should work in harmony.
Although we can find many places where it will work properly (interaction with satellite speakers will be in phase from the listener`s point of view), the positioning of the subwoofer is not completely arbitrary. We can reduce this inconvenience and increase the freedom of positioning the subwoofer by lowering the crossover frequency (the interacting waves will be much longer, and it will be more difficult to cause harmful phase shifts, for example 1/2 of a 100Hz wave has a length of about 1.7 m). You can also always reverse the phase of the subwoofer, even if there is no special switch or phase shifter system, by swapping the cables supplying the control signal. So this is not an unsolvable problem, but it is advisable to experiment with the setting and connection method.
[via some Google link with the entry speaker phase]