Wiki - The fuse element is made of zinc, copper, silver, aluminum, or alloys to provide stable and predictable characteristics. The fuse ideally would carry its rated current indefinitely, and melt quickly on a small excess.
and thus (or restated) it's end result of very high levels of non linearity, and production of odd ordered harmonics as a reflection, or final effect of it's behavior when dealing with dynamic current draw.
The cheapest way to a more linear draw is to go with a 'long lag' fuse in place of a short lag or fast blow fuse.
But such a substitution of a fuse type is not really all that 'legal' as rated fuses in gear also includes the lag aspects as part of their specification and use in that particular piece of gear. It is integral to the legal status of the electrical approval of the given device.
The question in audiophile fuses, is if the given audiophile fuse meets the spec required for that given piece of gear it is placed in.