Two flights, EK215/6 and EK225/6 (DXB-LAX / SFO) fly almost over the North Pole (max lat. 86 N) and a large airportless swath of icy sea and two other flights (QF63/4 and QF27/8) fly over remote airportless ocean from SYD to and from JNB resp. SCL. Yes, I know, it is ETOPS certified and an A380 should even not conform ETOPS rules, but, yet, emergency landings are not always option.
Imagine, when something happens on board (multiple engine flameout or, worse the horror scenario of engine fire or cargo basement fire), what happens when there is no airport accepting an A380 (SYD-SCL is 789) within thousands of miles ? Ditching into the ocean or landing crashing on icebergs in the Arctic, like the NZ case of the DC10 disaster in Mount Erebus in the 1980s ?

There are ETOPS-like restrictions that apply to three, and four, engine transport airplane flights. I have not flown a four-engine airliner since 2011 so am not current on the specifics. I doubt the nearest alternate will be thousands of miles away. Likely within about three hours, usually much closer.

Look at gcmap.com. Put in a route, map it, then scroll down and select the different ETOPS levels and redraw the map. It will plot the time arcs from each alternate airports. An emergency aircraft will be able to use airports that wouldn't be available for it to use in non-emergency situations so the number of alternates are not as restricted as you might think.

The risks of extended overwater operations are mitigated by many systems, procedures, and limitations.

Fire risk is mitigated with fire detection and suppression in all cargo areas. Engines are similarly protected with systems to isolate the engine (fuel, hydraulics, electrics, and pneumatics) at the pylons and to fight the fire with at least two activations of the fire suppression system.

Why would multiple engines fail? The aircraft systems are designed to prevent a single point of failure affecting multiple engines. Four-engine transports can also continue to fly with two engines out on the same side (worst case). If my search results are correct, the rate of engine shutdowns on ETOPS flights is about one per 50,000 hours of engine operation.

A single engine failure on a four-engine transport is not, in itself, an emergency. I had an inflight shutdown of the number 2 engine on a DC8 (four-engines), due to what turned out to be a faulty oil pressure sender unit, over the Indian Ocean. We continued on for a bit over four hours to our destination, Singapore, landing on-time and a bit under planned fuel burn.

It's easy to think of disaster scenarios. No system is foolproof, but instead, do some searches to see the actual performance of flights operated under ETOPS.

LarryJ�s response sums it up but I would like to note that the southern hemisphere is really quite empty. There is certainly a portion of the SYD-JNB route where no airport is within 3 hours flight time, possibly even 4.

The Boeing 787 is certified for 330 minute ETOPS, that's 5 hours and 30 minutes

The Airbus A350 XWB is certified for up to 370 minute ETOPS, that's 6 hours and 10 minutes.

The NZ DC-10 flew straight into Mt Erebus due to incorrectly inputted navigational information... it was irrelevant that it was a remote area really...given there were no survivors of the crash. The ETOPS system seems to cover the risks nicely IMO... And...in extremis large aircraft have been landed without loss of life on runways not really suitable for aircraft typer...or even no runways at all!

On GCMap.com, you can really see how those last couple of ETOPS levels really close up the hole where ETOPS airplanes can not fly.

Indeed. The details of the navigational error (not by the pilots) causing this Antarctic disaster in the late 1970s are well summarized here:

https://en.m.wikipedia.org/wiki/Mount_Erebus_disaster

Yes. I was responding to this from LarryJ:

For the routes being discussed those higher ETOPS levels are necessary precisely because the nearest alternate is, for the middle part of the route, thousands of miles and more than 3 hours away.

About 2,500nm at the most, and only that for short periods.

If the shortest route is taken, more than 3 hours for a significant period in the middle of the route:

A map from the Great Circle Mapper - Great Circle Mapper

A map from the Great Circle Mapper - Great Circle Mapper

of course the option always exists to fly a longer (more northerly) route to reduce the max diversion time.

I flew BOS-NRT nonstop both ways this past May. Westbound we flew over the northern coast of Alaska and came down almost along the western coast of Asia, Eastbound we stayed nearly at the same latitude for the entire trip. It would have been close to a straight line on a Mercator projection of the globe.

Bottom line is that winds can cause the optimal route for a specific flight to deviate hundreds, or for a long trip* literally thousands, of miles from the Great Circle route. Airlines are loath to deviate from the optimal route by much because fuel is expensive. Therefore, longer ETOPS range is important even when the GC route suggests that it might not be.
____________________________
*I'll fly AKL-JFK non-stop (QF 3) in just over six months. Not the longest flight in the world, but it will be the longest I've ever taken.

The eastbound route may have been affected by the closure of Russian airspace.

I've never heard of any Japan US flights availing of Russian airspace.

Not even over the Kamchatka Peninsula?

Not in my experience. I'd assume the fees would more than offset any fuel savings in pretty much all wind/weather scenarios.