People don't often talk about damping factor with regards to a midrange or tweeter, for good reason. It unfortunately it also commonly gets misused when describing the response of woofers. It's unfortunate naming:
damping factor, since it evokes lots of incorrect analogies to what is actually happening electrically. We have a
good thread on the basics. It's the ratio of the amp's output impedance to the impedance of the driver. And this is a discussion of a midrange/tweeter. I am not going to extend this to a woofer, that's a totally different post.
Let's look at what an L-pad does to a compression driver's impedance, and to the impedance of the resulting filter with the capacitor included. I measure the raw driver, the raw driver plus a filter capacitor, and repeat the measurements with and without the L-pad. Four measurements of impedance vs. frequency:
The L-pad negligibly raises the impedance below 400 Hz (red dotted vs. red solid traces) from 19 to 21 Ohms. This is nothing for a typical audio amplifier, which typically has 0.1 Ohm output impedance, even lower for some amps. Even if this was an 8 or 4 Ohm driver and was padded, still negligible for all but amps with
absurdly high output impedance.
What is significant is the taming of the three resonant peaks in the impedance in the 700 Hz - 3 kHz region. This can be seen in the raw response (red lines) and the total response with the filter capacitor (green lines). These untamed peaks do lead to actual audible response variations that need to be dealt with additional filters in the passive or active crossover. It would be wrong to say those peaks are areas where the
damping factor is really good, which is why DF is so misused here. It's likely some really high output impedance amps would struggle with the inductance of the unpadded driver, but amps with odd electrical characteristics is another topic.
Also, the L-pad significantly reduces hiss and noise. For the lowest noise amps (Benchmark, Hypex, PuriFi, to name a few), this isn't an issue. I
compared some low-noise amps to some higher noise models, since noise is an audible, and passive components like L-pads and capacitors can make a fairly significant and audible difference in a quiet room, which might be why JBL uses them in the M2 and other active models.
None of this is elevator music only applications. The DF problem doesn't even closely apply to this application, there are other order of magnitude larger issues to deal with.