It is indeed that type of fuse at the IEC inlet and that is there to protect the equipment.
The power supply inside the equipment will influence sound quality.
The rating of the fuse in the mains plug needs to match the cable. So, for example, a 13amp fuse with a mains cable that is rated 5amps is not going to stop the cable overheating should it suddenly encounter more current than it is capable of carrying.

If manufacturers of mains plug fuses would like to set up a double blind listening test I am a willing volunteer for the panel. I will even pay my own train fare.