Because power dissipated is proportional to current squared!
Energy dumped into the fuse element is proportional to I^2 multiplied by time if you assume the fuse is a resistor (Not a safe assumption, but close enough).
Note that there are at least two implicit assumptions here, first that the resistance remains constant as the fuse heats (Ha) and secondly that the losses are negligible both to radiation at higher temperatures and via conduction to the end caps, neither are really safe assumptions.
Fuses are actually surprisingly complicated, and some have fascinating metallurgy where the alloy composition actually changes before failure.
Regards, Dan.