[kmm]

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.

[OkayPhysicist]

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.

[sobriquet9]

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).

[magicalhippo]

Works other way too. For me the explanation of a hydraulic ram pump[1] clicked when I realized it's essentially just like a boost converter[2].

[1]: https://en.wikipedia.org/wiki/Hydraulic_ram

[2]: https://en.wikipedia.org/wiki/Boost_converter