To
@Tangband 's point, I think you actually need the electrical filter even if you use DSP, for the reason
@fpitas mentions. If and when I get around to building any decent speakers, I intend to (try to) implement this.
From what I have ready on DIYAudio, this "trick" really helps with high quality metal drivers, which tend to have a sharp but controlled break-up region. Cross over well below the breakup and notch out the resonant peak, and you magically end up with less distortion below the filter frequency. The fact that this works is somewhat beyond my understanding of electronics, but it seems intuitively plausible anyway...
Think this: you have DSP low pass filter at 1kHz and play a sine tone at 1kHz. There is cone resonance showing peak in drivers datasheet at 3kHz, well above low pass filter. The resonance peak is 10db. Important thing to understand here is that the peak is not the amplifier boosting it, its the driver (cone) that amplifies any signal, so any 3kHz current through voice coil gets additional 10db boost in acoustic domain. You can reduce the input signal by 10db with DSP, and it gets boosted back by the driver in acoustic domain, and we measure smooth response with a microphone for the input signal, cool.
Now, the driver motor has varying parameter like voice coil inductance Le(x) which changes with excursion, and as you crank up the 1kHz tone the voice coil moves, Le changes and third order distortion component at 3kHz is induced into the voice coil as current. Current in the voice coil turns into voice coil movement at the very moment, is amplified by the cone resonance and you'd see high 3rd order distortion for 1kHz in distortion plot. This all happens after the DSP and it can do nothing about it. The distortion is probably similar with any frequency and similar excursion, thing here is that at 3kHz the cone resonance works as amplifier and elevated distortion reading ensues.
Driver motor non-linearity makes this distortion in impedance, which means with constant voltage input that current in the circuit varies with the nonlinear impedance, the distortion appears as current and emits acoustically right away. Reduction in distortion in acoustic domain can happen if current at 3kHz is reduced in the voice coil. This is another key thing to understand, the parallel notch filter needs to be in series with voice coil, same current flows through both simultaneously. The parallel notch filter in series with the driver increases circuit impedance at 3kHz reducing current through voice coil at 3kHz, including distortion current originating in the driver motor. Now also any distortion products that appear in the electric domain are EQ:d.
In general, one could increase circuit impedance also with a series coil or just with a resistor, or use high output impedance amplifier, what ever, to reduce distortion originating from driver motor. The parallel notch is handy for the breakup peak.
Not sure how audible this is, yet to listen this myself. I've got active system, having series coil as low pass in addition to DSP but not sure I hear any difference, its pretty low distortion system anyway. You can find out more about the subject by looking into current-drive. Read the Purifi paper again as well, also their other material available on the website. Hope it helps
edit.
As disclaimer I'm just a hobbyist and above text might have errors but this is how I understand the basic mechanism behind distortion reduction with circuit impedance, based on Purifi papers and other resources.