As was stated above fusing is a safety issue: to protect your house from fire in the case of certain component failures and to aid in keeping 120V (or whatever) from being present in the case of a component that has some weird fault inside (like a knitting needle from a kid or being peed on by a cat.)
Fuses of necessity are non-linear devices (they have to act fundamentally differently for high current than low current) and any non-linear devices can affect audio in non-obvious ways. At the least they may modulate the current available based on the power drawn. Since hearing can at times have more resolution than approx. 1 part per million it’s sometimes possible that the small modulation caused by fuses to be audible. Nothing is perfect so even that modulation back at the regenerator might be audible. But more likely is that various fuses dampen high frequency garbage differently than 60 Hz AC. High frequency garbage travels much more easily along parasitic capacitances and inductances in devices. And non-linear components can modulate some of that high frequency hash into the audio band.
Some speakers may be fused to keep too high of a current demand from frying some part of the speaker, either in the cross overs or the drivers. Or potentially save your speaker wires or amps if there’s a short in the speakers.
It depends on how accurately you are using the word impedance. At the high level a fuse is a non-linear resistor, low resistance for low current and in the limit infinite resistance after too high of current for too long. Impedance is most accurately used to model the changes in phase and amplitude of a component/system at different frequencies. None of this is very useful in the typical modeling of fuses. (Tho as I alluded to above it might be subtly relevant for high frequency noise in audio systems.)
Re speaker fusing: a couple of decades ago we had a power glitch when I was using my system. When the power came back on the TV that was between my speakers had very colorful “rainbows” all over it. It had been “gaussed” by a high current flowing thru my speakers. One of the speakers was silent and it took a while to find that one of my speaker wires was melted like a fuse at one point. With a new speaker cable the amps and speakers turned to be fine and by turning the TV on and off a number of times the degaussing circuits slowly brought the display back to normal.