Some data showing a benefit of also using a High pass filter when using a subwoofer.
Was that a question? A crossover is standard. Every Home theater receiver has a crossover for the subwoofer output.
The standard set-up uses "bass management" to re-direct ALL low-frequency information to the subwoofer so you can use "small" main/surround speakers. If you turn-off bass management, the full frequency range goes to the 5 or 7 surround speakers unfiltered, and ONLY the LFE (low frequency effects) go to the subwoofer.
If you add a subwoofer to a regular-old stereo system, there often isn't a filter/crossover for the original stereo speakers but that's not a "proper" setup.
Yes there often is not a crossover,and so the owners of such things do not get the be benefit of mid range clarity that a sub can provide. The reduction in IMD is visible in the charts in the link. That is for a 3 way speaker plus a sub , so it seems reasonable to expect that the data for the improvement for a two way speaker would be greater still.