It just occurred to me that curiously one might prefer a tweeter pad resistor(s) that exhibits significant temperature/power related issues, as if you get it right , it could balance the dynamic resistance change of the voice coil. Virtually impossible to design from first principles, but I could imagine situations where this could be a real effect, and choice of exact resistor specification, coupled with its physical environment in the speaker cabinet could affect the dynamic frequency response.
If you talk to the guitar tube amp guys, they actually prefer carbon composition resistors. There is much argument, much Mojo, most of it that the older amplifiers all were built with them, and thus to get the vintage sound you need vintage parts. Most old amps were built with the cheapest parts the manufactures could get a way with, which isn't always a god start. Guitar amplifiers can have a sound that is partly dependant upon poor design practices or underspecified parts. But there is also known physics, carbon composition resistors have lots of contact noise, and this noise is modulated by the signal across the resistor.
Link. They also have very a poor temperature coefficient, and generally poor long term stability.
Link.
As above, signal related changes in value can create intermodulation distortion.