Eventually you need to pullin a physicist too who will point out that at an appropriate distance quantum effects will dominate - because eventually at a far enough distance the number of electrons moving per second (ie current flow) will be either 0 or 1 at some nodes
I don't think you'll ever get 0/1. You get a difference in voltage that influences all electrons to move slightly more in one direction than another in electric current. They'll just drift very very slightly as a group, not measurable when you get far enough. But they're always all affected, rather than individually.
Intuitively I knew this class of problem was theoretical only BS when it came up in college...
I hadn't considered that sort of strange effect though! Makes me feel not so bad for 'never really getting it' because I just couldn't wrap my mind around the problem description's obvious inanity and the infinite edges.
The question is not pretending to be realistic. No one is thinking it is possible to build an infinite grid of resistors.
It's simply an evaluation of your mathematical ability to manipulate the equations and overall understanding of them, wrapped up in a cute little thought experiment. This evaluation IS relevant to more realistic scenarios and therefore your grade and engineering ability.
I've not studied QED directly, so by all means correct me if I'm wrong, but it seems to me that we'd get a double-slit like scenario where it's as if a partial electron went through either path. We might want to say that surely a whole electron took one path and not the other but we couldn't say which and if we tried to instrument to and find out we'd affect the resistance.
But that's fine because knowing which path the electron took is not part of the problem. Both paths contributed to the resistance even if one was not taken.
We only have to worry about quantum effects if the probabilities are not a decent proxy for the partial-particles that we suspect don't exist. In this case, the Physicist can probably proceed directly to the bar and have a drink with the Mathematician.