Compression drivers are notorious for producing large amounts of 2nd order distortion, especially if you push them a bit too low (what this looks like). Luckily you need copious amounts of it to be audible and even then it's unlikely to sound bad.
It isn't perfect but I'm guessing that no one will hear it.
I suspect you are right. My JBL Studio 590's and 580's use their 2414h-1 driver which has 98db sensitivity; by their own specs, the recommended minimum crossover frequency is 1.9KHz for that driver. In both towers, the crossover is at 1.5KHz and the crossover has a serial notch filter to dampen the resonance ( a band aid that would not be needed if used within recommendations). Reviews have shown a resonance near the crossover, so the band aid is not totally effective.
I can't say how much it affects the sound, but in my mind, I would prefer to use drivers that can work within limits.
I built a center channel to go with these towers since JBL does not have a capable Center for this series and used a B&C DE250 that has 10db higher sensitvity, a larger diaphram and has a minimum crossover of 1.5 KHz. Being padded down 15db to match the midbass and all of the other factors above, it is pretty much cruising at any level that the 590's can play. It ended up being a higher resolution speaker than the 5's.
Of course, I was not working to a price target; at the usual 4X markup, this would be a $1500.00 speaker.
JBL has more capable compression drivers, but the resulting speaker would be more than the current overpriced ( in my mind ) models they have.