The electrons are only moving at ~ mm/s. With an AC current, the net effect is that they're not moving at all. Electrical power is not provided by the movement of electrons. The force carriers of the electrical field, the particles responsible for actually exchanging energy, are photons.
I initially was mostly interested in the word instantly, but if we're going to analyze this analogy further, I'd have to say you just can't treat electrons inside bulk materials as particles. It may sound sensible and give you the idea you understand what's going on, but it's just not even wrong.
Umm, yea just like the marbles in the example. If you have a marble pushed into a pipe with 1,000 marbles the one popped out at the end is pushed out a lot faster than any single marble moves.
Ummm... no? It'll come out at roughly the same speed (less if the moment it came out there was still energy trapped in the form of compressed marbles when it emerges). Why would it be otherwise?
Have you ever seen those desktop toy's where steel balls 10+ steel balls are strung up next to each other. You drop one and it fall hit's one end of the chain and in less time than it would have taken the first ball to move that distance the last one pops off the end? Same concept the final ball moves a little slower than the first ball that hit the chain, but it start moving sooner than it would have taken the first ball to move the distance of the chain.
Ok that's true, but not how I read your post. Yes the energy is transfered at the speed of sound in the material, but I read your post as saying the velocity of the marble on the end is greater than the velocity of any other marble, including the one you push in, which is certainly not true.
I initially was mostly interested in the word instantly, but if we're going to analyze this analogy further, I'd have to say you just can't treat electrons inside bulk materials as particles. It may sound sensible and give you the idea you understand what's going on, but it's just not even wrong.