I've just installed an electric fence (actually a net for keeping sheep/goats within a pasture), powered by a 4.8J supply. With three earthing rods 1m (3ft) deep, spanned 10m, it should be enough for a fence tens (theoretically hundreds) of kilometres long, depending on vegetation touching and discharging it.
The pasture for our goats is much smaller. But I wonder how it could work in such a distance? Imagine a furthest point some 30km (18miles) away. Does it really matter if there are some rods in the ground if they're so far from the place of discharge? It's hard to imagine it - even with almost 10kV voltage.

Yes, it does. Ironically the greater the distance, the lower the relative Earth resistance is. In fact you may even say the Earth resistance alone is zero, all you see is "contact" resistance of your earthing system (plus the hooves of the poor sheep or goat that decided to try to go too close to the fence). As that is how the resistance nehaves with distance.
By tye way in some rural areas of tge world (USA, Australia) to cover the larger distances at low cost were used power distribution systems called SWER. It is a single wire, really using Earth as the working return conductor. Voltages were in the 20..50kV range, currents bellow 10A.
Or many submarine power cables use Earth (or the sea water) as the return path as well, but only in some fault cases (mostly these cables run in pairs for redundancy, but connected so the ground current cancels out during normal operation when both are working).

So for a fence, I would not worry about the Earth resistance. The thing to worry about is rsther the wiring resistance and mainly the total capacitance (the whole net will exhibit way larger load capacitance than a few wires) and leakage of such large fence for a single supply unit...
Mainly with sheeps, where you need rather high peak voltages to be effective...

Interesting! Didn't know that something like SWER existed.

Animals quickly learn to avoid electric fences so there'll be almost no accidents soon. It's quite unpleasant, tested it on my finger.

The only nightmare is a bloke firing noisy fireworks or chasing them with a drone. The animals could stampede into the fence, get stuck and tormented until their rescue or death.

Pur pasture is 3km away on a pretty poor dirtroad. There are GSM monitors (expensive like h...) reporting a voltage drop and GSM remote switches.
I'm  thinking about installing a time switch on the very low voltage part (the supply is powered from a 60 Ah AGM accumulator) because goats sleep ať night and the only risk is that stampede.

Animals do learn, otherwise such thin rope on flimsy poles would not stop them.
But they also learn to sense the pulses and the pulse timing and how to push away tge rope by their thicker furr. So if it would not reliably shock them even through the thickest wool, they will find the way to defeat it without actually getting shocked...

Animals indeed analyse the fence to find the weakest point. Goats are true "Houdinis", managing to open various keyless locks and also how to pull up the electric rope with their horn and escape. That's why at least 5 ropes are recommended or even better a net (like OVINET) which is our solution. The net also works in the opposite direction, protecting them from wolves etc.
The downside of the net is that they might jump into it in a panic and get stuck as said in the previous post.

I've noticed an interesting effect. A part of the electric fence (some 50m/160ft.) goes along a non-electric fence with wooden bottom and steel wire netting above. The distance between the fences is about 1m (3ft).

Guess what happens!