The issue is a dearth of test data for power losses of inductor cores used in crossovers. I have been contemplating running some tests on inductors used for audio, but power analyzers are not cheap and I am now retired. I may pickup a used one and get it calibrated.
Long ago, early in my career, I was tasked with figuring out why inductors were overheating in powerline filters running at 60Hz and 400Hz. They used laminated silicon steel C-core inductors with 12 mil. (0.3mm) and 4 mil. (0.1mm) lamination thicknesses, respectively. I ran numerous tests to isolate eddy current power losses from hysterises losses, and from that data derived constants for use in equations to accurately compute the power losses. I don't have a copy of the report I generated as it was considered by the company to be a trade secret. But, I can say this, the inductor core power losses were significantly higher than those previously computed. Specifically, the hysterises losses were much higher than expected. Previous assumptions that thinner laminations reduced eddy current losses, and that power losses increased significantly with frequency, were confirmed to be correct.
In audio, laminated steel inductors commonly are used. The cost effective cores typically used in mass produced speakers have thicker laminations (maybe somewhere around 0.4mm - 1.0mm, depending on the crossover manufacturer) of what I suspect is cold rolled steel. The more expensive ones use thinner laminations of silicon steel, resulting in lower power losses. Air core inductors have no core, and thus don't have any core losses.
At one point when I was in audio engineering, we conducted a blind test comparing inductor cores. There were three of us, and all of us clearly heard an audible difference in the upper midrange. The difference was not subtle with that inductor value in that two-way speaker.
An issue that I commonly see is that people see test results of capacitor comparisons, and just assume that the same results apply to inductors. That is a falacy. Inductor hysterises has a much more significant impact on power losses and time domain response than capacitor equivalent series resistance (ESR) and dielectric absorption (DA).
Another issue I commonly see is that people see a comparison showing a particular result, then assume that result applies to all similar comparisons. That is not always the case. Erin's Audio Corner did a video on that regarding amplifiers.
I spent a good portion of my career designing filters, including designing the inductors and capacitors used in those filters. I am happy to never again use passive filters in my speakers, primarily to avoid use of inductors in my crossovers.
