The hydrostatic analogy helps a person understand the difference between voltage and current. But its real power is it gives you the building blocks that lets you understand more complicated behaviors by analogy.
Take power in the P=I*V sense. Pretending it's water, we can see how a supersoaker nozzle (ie high voltage, low current) is kinda moving the same amount of water in a unit of time as say a soda bottle tipped on its side (ie low voltage, high current). With the hydrostatic analogy, I can see how high voltage and high current are two different "things", AND I can extend those analogies to see how they explain additional concepts like power. That's a great mental framework! Now that I understand the basic dynamics and feel comfortable moving into the land of mathematical expressions, we can take off the training wheels and start talking about the really abstract stuff like capacitance.
On the other hand, I'm not sure what is the explanatory power of this "meshing gears" analogy. If you were to use this to explain electricity in say a high school physics class, what concept or insight does it help me grasp?