Are Maxwell's equations useful? Electric wires are very unlike the situations you deal with in an electromagnetics class, and conversely there are phenomena no electrical engineer ever thinks about, like the fact that a voltage drop over a resistor means there's a nonzero charge distribution at its ends, and similarly surface charges on the wire have to carefully redistribute themselves around bends in the wire to guide the electrons along it. Unless you work with gigahertz electronics, none of the interesting electrodynamic transient behavior matters either, the circuit always instantly finds the steady state distribution.
That the water analogy works so well also has little to do with the Maxwell equations, if I'm not mistaken, I think it has more to do with the conduction electrons behaving more or less like a (highly degenerate) gas.
The water analogy works because circuits are linear systems. Pretty much all linear systems can be modeled that way, if you're willing to contort things the right way.
Water analogy works well even with non-linear components like diodes (think one-way valve) and transistors (think valve controlled by water pressure from separate tube).
For a layperson, Ohm's law and Kirchhoff's laws suffice.
You don't need curl and divergence to figure out whether you can turn on your microwave and coffee maker at the same time without tripping the circuit breaker.
This is only true because someone who did understand the more complicated principles designed the appliances in question. High voltage and high frequency are where the most common and intuitive understanding of electricity break down. Anything above about a megahertz or a few hundred volts and you will start to see relatively strange things happen.
My point is that few people work with high frequencies.
For most practical tasks, even the fact that we're working with AC rather than DC can be glossed over. People can plug in 120 V into Ohm's law and get the right result even though actual voltage fluctuates between -170 V and +170 V.
That the water analogy works so well also has little to do with the Maxwell equations, if I'm not mistaken, I think it has more to do with the conduction electrons behaving more or less like a (highly degenerate) gas.