Fuses have to heat up and blow to protect the downstream equipment. So they have to have a significant resistance (to heat up) and as current goes up, they heat up, resistance goes up (a property of all metals) and they heat more and blow. This isn't a problem for electric motors or household equipment. but a high end amplifier can have dynamic changes in power requirements over a very short time which can be limited by the fuse. If this happens to your air conditioner, it will still cool. If it happens to your amp, it will still make music, it just won't be as dynamic. Bass will suffer as well.
An audiophile fuse supposedly has less resistance and limits current less. I have never bought one and don't plan to.
I replace fuses with slugs. an overcurrent situation in an amp is very unlikely and when it does happen it is usually caused by user error. There is a very audible difference in most amps replacing the mains fuse. This is especially true of tube amps. Also if your amp has fuses on the rectifiers they should be replaced.
No your amp won't burst into glorious flames but if you can't get this image out of your head, keep your fuses.
I have tested the Swiss Digital Fuse Box that replaces the fuse with a magnetic current sensor and a relay, thus there are no heated components in the power circuit. My opinion of this piece was that it was better than any fuse but not quite as good as a slug. It is also cheaper than an audiophile fuse.
Jerry