The relationship between the amount of overload and how fast the fuse is supposed to blow is quadratic, not linear. As an example with somewhat made-up numbers,

The relationship between the amount of overload and how fast the fuse is supposed to blow is quadratic, not linear. As an example with somewhat made-up numbers, at 1x it might take hours to blow, at 2x it might take a minute or two, at 3x it shouldn't take more than a second and at 4x it should be nearly instant. If it's supposed to blow in 0.1 seconds when overloaded by 4x, then taking 10 minutes is many orders of magnitude in my book. While that fuse is taking its sweet time, wiring or other components are being heated out of spec (16x more heat at 4x the current), potentially posing a fire hazard or damaging the device it's supposed to be protecting.