He asked for the advantages of using a NON-fusible vs fusible, not the other way around.
There is only one "advantage" so to speak. If you ALREADY have a valid Short Circuit protective Device (SCPD) such as fuses or a circuit breaker somewhere upstream in your circuit, DEDICATED to that single circuit, then you do not need an additional SCPD downstream. In fact it becomes a bad idea to have too many SCPDs in the circuit because you create possible confusion as to which one opened, which increases the risk of a safety mishap.
So an example would be, you have a motor controller circuit. Power for it comes from a distribution board via a properly sized circuit breaker. All wiring is correct for that size circuit breaker out to a local control panel. You are required to have a lockable external disconnect at that control panel, but at that point, fuses would be redundant to the upstream circuit breaker. You don't absolutely need them.
That said, some people may put them in anyway because often times, fuses provide other beneficial capabilities, i.e. current limitation and/or faster clearing for semiconductor devices.