A few things come to mind.
The L-pad smooths out the driver's impedance peak.
Here is the impedance of a D2 driver mounted in it's lens with no filter (blue), the L-pad only (red), and the complete network (green):
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Some amps may become unstable with this high impedance.
The impedance resonances do change the frequency response which could be addressed in the DSP filters.
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But the L-pad appears to be damping the resonances seen in the impedance curve, especially in the red trace where I drive the speaker with only the 8 uF filter capacitor and no L-pad. You can see in the red trace the impedance peaks are interacting with the filter capacitor and making additional response unevenness with higher peak at 600-700 Hz, lower trough at 800-900 Hz, and a larger ripple in the 1-2 kHz region. This translates to less filter EQ needed to get to the desired response. Those closely-spaced ripples are hard to EQ. The cost is 9 dB less voltage sensitivity, which in the case of this driver is actually an advantage for me since it plays absolutely terrifying SPL with just a few Watts.

I reduced the gain 9dB for the measurements without the L-pad.
The impedance resonance anomalies are often best removed at the source in my simple experience, although am not an expert on resonances in non-linear systems. I do see a spike in 2nd HD at 600-700 Hz with the 8 uF capacitor, but it really isn't dramatic. I would be interesting if Dr. Toole or maybe
@Frank Dernie have comments or considerations about damping these resonances with the L-pad.
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This is no big deal on distortion, even if we can see a spike. Perhaps at higher SPL this becomes more dramatic due to nonlinear behavior of these resonances, JBL likely have data but out of self-reservation I won't test that loud!
Thatt 9 dB reduction in sensitivty can be an advatage, the network reduces audible noise allowing the driver to be powered by a range of amplifiers even with elevated noise specs. I actually compared the noise of the driver with and without the passive crossover across a range of amplifiers; PuriFi, Hypex, Bryston, Marantz, and a 1979 Aiwa micro integrated amp

.
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I put the mic at the face of the D2 lens, measured ambient noise with an without the L-pad, and compared to the other noisier amps using the L-pad. The Aiwa was thrown in for fun, but actually has acceptable noise with the L-pad. Sorry that the graph is busy with poor colors. Basically the L-pad takes an amp that has barely audible noise like the Bryston and makes it inaudible unless I stuff my ear in the lens.
I think the capacitor for both 6dB/oct filter and DC blocking is a great implementation.
I guess the drawback is if you need a larger amp to account for the 9 dB loss in sensitivity. You also need to change the filter capacitor if you want to change the DSP crossover since they are integrated, but this is minor.
I also think it is a tremendous sounding speaker.

So whatever drawbacks, I think are offset by other tradeoffs.