When power supplies and transformers are turned ON the inrush of current is very large and you will see tiny fuses such as 315mA, stretching and dipping. This has the effect of weakening them and quite often they fail after a period of time for no reason.
Secondly, a small fuse will take a lot of current to actually burn out and merely shorting a low-current supply will not cause this current to flow and nothing will be protected. The supply will just over-heat.