Fuses don't dissipate electricity. They pass electricity and then blow when exceeded. Blowing is either flipping off (like your breaker) or breaking (like replaceable fuses). The point of a fuse is to be the weakest link so if a surge occurs it doesn't damage equipment or wiring.

In the case you described, they were looking for a load (where energy is used or dissipated to do work) to absorb that much energy at once. There might be a fuse that could withstand that kind of load; there was wiring that could afterall. But if the shield system could absorb the full power of an overloaded warp core, it might not have needed one if there was no downside to overcharging it.