The thing is that KVL and KCL hold, and KVL and KCL hold for both electrons and water. You just have to not think too deeply about what motivates the electrons

The thing is that KVL and KCL hold, and KVL and KCL hold for both electrons and water. You just have to not think too deeply about what motivates the electrons to move. Current is indeed the mean velocity of carriers through some area, and voltage is mmm... well it's related to the electric field. It's just not exactly fluid pressure even though it behaves as such. The right way to think about this if you _really_ care is a bit like the way that RF engineers think about dielectric resonators. The metal motivates the fields to be guided along pairs of conductors by the motion of charge carriers within. A metal will respond in a particular way to fields, which results in new fields, and so on and so forth in a way that results in the fields propagating along in a particular way. A propagating pulse is a bit hard to think about but you can imagine some field configuration that results in the electrons in the metal slipping a bit, and those electrons move in a way that results in new fields which contain the new wavefront of the pulse. The electrons don't keep moving -- they move on average the distance of the mean free path and give their energy to the lattice as heat. This is why the drift velocity is just a meaningless number. The fields propagate at around c and the conductors guide them.