BEWARE THE SANDWICHES!!!
In the spirit of math-avoidance sandwich-juggling, here's a better analogy, a visible one. The movable charges within conductive circuits are like silver bead-chains, like those little chains which attach the pens to desks in old-school banks. (Growing up I always played with these when mom was in the teller line. Do those bank-pen chains even exist anywhere?)
Obviously these bead-chains can transmit pulling-forces like any chain. But they also can transmit "push," if we compress the chain so all the beads are lined up and touching together. Electric circuits do both, and so do the bead-chains.
Make a drive-belt using a loop of bead-chain, with two pulleys, and two pipes. (The chain is inside the pipes, so the beads are forced into a straight line.) Now turn the drive-wheel. It compresses one side of the chain-loop. The solid column of beads grows outwards, and you can watch the wave move along to the far wheel. The drive-wheel's rotation also yanks on the other half, and that side of the chain will progressively un-compress. A wave propagates along both halves of the chain-loop, from drive-wheel to driven-wheel, and when the waves arrives at the driven wheel, that wheel turns also. Reverse the drive-wheel, and the waves still go in the same direction, going from drive-wheel to driven-wheel.
Note that these chain-waves move much faster than the beads themselves (the electrons.) Also, the waves move along both halves of the loop, going in just one directino from the "generator" pulley to the "motor" pulley ...while the chain itself moves in a complete circle, with half of the loop going backwards against the wave.
The wave is the joules. The chain is the coulombs. The speed of the chain is the amperes.
So, there's your answer. The drive-wheel "knows" what's on the far end because the beads stack up on one side and produce back-pressure. The drive-wheel can "feel" the distant driven wheel, feel whether its free, or stalled, or resisting. And on the other side of the circuit, the beads all pull upon each other, so any resistance at the driven-wheel becomes known to the whole chain, regardless of which direction it's rotating.
Note that both halves of the beads-circuit are transmitting energy. There's no "return wire" filled with useless "empty children" which carry no sandwiches.
Note that electrical energy is a wave, and the row of charges are the medium through which it propagates. (And, the entire circuit comes pre-filled with charges.) The slow speed of amperes and the fast speed of wattage is mysterious unless we realize that electric circuits are a wave-and-medium situation. Of course the medium moves slow. Usually the medium doesn't move forward (or backward) at all, instead it just vibrates, while only waves actually "flow." The electrons in wires are a medium for propagating waves, and the waves are the electrical energy. The energy doesn't stick to individual electrons like tiny sandwiches might. Without this key insight of wave-and-medium, we'll always end up with some confusion about watts versus amps, and about joules versus coulombs.
For AC circuits things are much clearer: the coulombs wiggle back and forth, while the joules move continuously forward, it's waves moving through a medium. Unfortunately many grade-school textbooks (and your teacher) ignore all this, and try to teach circuits based on DC, where all of the fast-moving wave-energy becomes completely smooth and invisible. No, batteries and bulbs are not simpler, instead use AC generators with bulbs, that way the fast waves are a major issue. Or, at least use a DC hand-crank generator, and wiggle the handle violently back and forth to light the bulb.
Try doing the "sandwiches" with an AC circuit, and you'll see how it all falls apart.
The sandwiches don't work, since the electron-current in metals is a very slow flow, yet the lights turn on instantly. How did the "sandwiches" get there so fast, if the kids can only inch along at feet-per-hour rates? The kids must be handing off; transferring rapid sandwiches between children all along the line! And, for a proper circuit you'd need a complete circle of kids, with half of the kids facing the wrong way, and sending their sandwiches to the kid behind them.
When the two streams of sandwiches meet at the distant load, they're converted to heat. Must make a big sandwich pile, and set them on fire. All-meat subs with extra olive oil, they'd go up like a torch. Keep it accurate though: as the pile burns, continuously deposit more sandwiches so it doesn't get any smaller.