The problem with this analogy is that pressure waves can only travel in a medium. The pressure wave exists because the particles in the medium bump against eachother to propagate energy so the analogy gives people the impression that electrons are bumping against eachother to propagate energy. Photons are distinct entities that can travel without a medium. See michelson-morley experiment. Electricity is nothing like what we experience on our macro scale. Analogies never convey the full story.
The analogy does not completely explain the actual behavior of electrical current, that's true. But what's more important, and what it does clearly show, is that a fast wave can exist without fast movement of the particles involved.
> the analogy gives people the impression that electrons are bumping against eachother to propogate energy.
If this is not approximately how electricity works, why does the current stop flowing when you disconnect the wires, or equivalently when you "connect" them via something that doesn't have free electrons (i.e. an insulator)?
TL;DW: the power is transferred by the electric fields, it's the electric fields which move the electrons, if there's a break in the circuit the electrons necessarily accumulate in the places that minimise the electric fields.
Unfortunately the explanation to your question is something that takes years of education to understand and even then, most people just come out understanding some parts. The best I can do on an internet forum is tell you that the analogy is wrong, because experiments told us its wrong. My advice is if you want to understand this stuff, do the math! ;)
