You're trying to describe some complicated things and seemingly understand them in simple terms.
I'm not at all surprised that a Focal crossover is doing weird things to get the amplifier to push more or less power. That's how they mitigate aberrations in the performance of the drivers. My assumption finding something peculiar in a Focal crossover would be that it's trying to control a particular trait of the speaker.
Damping factors tend to be a little more complicated than the number except in a very simple amplifier. Virtually all solid state amps degenerate the output devices with resistors. That tends to lower the damping factor. Feedback loops tend to fight against the degeneration by making the the voltage gain stage, itself often degenerated, compensate for the truncated gain characteristics of the output devices and raise the damping factor. The result is more complicated output impedance characteristics than a damping factor rating might imply.
Since most amps have feedback, and that's where they get a significant amount of their damping factor, it's reasonable to assume anything presented as a load to the output will influence the momentary damping capability of the amp. However, wisely implemented feedback will do what feedback should do; simply control the load.
Looking to the measured properties of a variety of cables seems to suggest that those building them have some understanding that adding impedance and capacitance does effects the sound. Typically they go for the higher capacitance to ameliorate inductance since an amplifier's damping capabilities are more robust at lower frequencies.
That's my line of thinking at least.
I'm not at all surprised that a Focal crossover is doing weird things to get the amplifier to push more or less power. That's how they mitigate aberrations in the performance of the drivers. My assumption finding something peculiar in a Focal crossover would be that it's trying to control a particular trait of the speaker.
Damping factors tend to be a little more complicated than the number except in a very simple amplifier. Virtually all solid state amps degenerate the output devices with resistors. That tends to lower the damping factor. Feedback loops tend to fight against the degeneration by making the the voltage gain stage, itself often degenerated, compensate for the truncated gain characteristics of the output devices and raise the damping factor. The result is more complicated output impedance characteristics than a damping factor rating might imply.
Since most amps have feedback, and that's where they get a significant amount of their damping factor, it's reasonable to assume anything presented as a load to the output will influence the momentary damping capability of the amp. However, wisely implemented feedback will do what feedback should do; simply control the load.
Looking to the measured properties of a variety of cables seems to suggest that those building them have some understanding that adding impedance and capacitance does effects the sound. Typically they go for the higher capacitance to ameliorate inductance since an amplifier's damping capabilities are more robust at lower frequencies.
That's my line of thinking at least.