, if one inch of hair thin cheap wire does not degrade sound quality then why waste money on good wire anywhere?
cheap has nothing to do with it, that is hyperbole for dramatic effect
in order for it to work the fuse has to have a certain amount of resistance. The energy flowing through it would not heat it up if it did not so it would never blow. So any fuse is going to consist of a "thin wire" of some length. Unequivocally stating that this will degrade the sound might seem like a logical conclusion, but without some kind of proof it is a mere guess.
And the speaker cable analogy makes no sense and is irrelevant because what is a small amount of resistance in an inch of wire would be too much resistance in many feet of the same wire