If a device only draws the amount of Amperage [amps] it needs, than why do we have fuses rated 13A and 5A etc?

Because i'm always told, its the Voltage that matters and the Amps need to be the same or higher to run a device, like an electric fan. But then why do we have fuses to avoid higher current/Amps, if high Amps don't matter for a device? Thanks, this question was really bothering me.