The answer is actually quite simple, it's because you can assume the power a fuse fails at is constant and that a fuse has a constant resistance. This is because a fuse is usually just a wire that will melt at a certain temperature. Below is the math to prove it.

- ConstantPower = Voltage x Current
- ConstantPower = (Resistance x Current) x Current (using Ohm's law)
- ConstantPower = Resistance x Current^2
- ConstantPower = ConstantResistance x Current^2
- squareroot(ConstantPower/ConstantResistance) = Current
**Constant = Current**

As a reminder, this is true even if the fuse had a very high resistance, as long as the resistance is constant.