I expect this is desired for a few reasons - heavy military airlift, to match what the US has had since Vietnam with the C-5 Galaxy. Access to licensed construction of the D-18 engine (as mentioned by ovi256). And ego.
Saturn-5, one of the biggest rockets so far in the world, was manufactured near a river and transported by a big ship. This sidestepped the problem of roads.
Energiya, the Soviet heavy rocket which launched Buran, had its huge second stage flown by a plane to Baykonur.
In 1960-s, USSR was looking for a good solution to this problem. They considered building a huge canal to use ships; they were thinking about using an aircraft; they played with an idea of building an exceptional - biggest in the world, if I'm not mistaken - automobile to carry it over desert. Eventually they decided to build rocket near the launch complex - that's the reason N-1 has the unusual shape.
Today, SpaceX keeps lengthening Falcon-9 modules - but it can't make them wider, because existing roads won't allow it. Long stages have their share of problems - they could be less efficient by mass, they could have unwanted dynamic characteristics - imagine a long thin-walled container pushed from behind through the atmosphere, it way vibrate...
In short, just the rocket industry of the world alone - that's currently about under hundred launches per year - could provide the market for big planes. At least this is a possible option.
It's not just the size, it's also the shape of such airlifters that makes them non-economical for commercial use.
For example the USAF's own data shows that the C-17 burns more fuel per hour than the KC-10 but carries 20 tonnes less payload by weight, all because of the fat rear-loading-for-tanks fuselage ( that's seldom used for such ) and thick wing.
Both the C-17 and the C-5 were touted on the civil market but had zero uptake.
As you see, fuel economy is somewhat worse compared to that Boeing.
I don’t think the main problem is size or weight. I think the main one is age. AN-255 is 30 years old, Boeing 747-8 is 6. That’s almost 25 year or progress in aerodynamics and engines development.
If the plane were economical for general cargo lift they would have made more than one.
1. You can carry huge tanks (instead of several smaller ones), including ones that were NOT intended for that, meaning you can surprise an enemy by deploying some weird weapon where he doesn't expect.
2. You can carry trains, and then use those to carry the rest.
3. You can carry other airplanes, for example if you end in a war of attrition and need to crank out planes as fast as possible, it might be an interesting idea to make them even far from the front, and ferry the plane parts to the front (then assemble there, and use them).
4. And most interestingly, it can carry gigantic parts of whatever you need, warship propellers, munition factory machinery, and so on...
It is tempting to think it would be interesting to use as bomber or paratrooper plane, deploying a huge amount of bombs in the same place and levelling it completely... but this would be a terrible idea, a plane that big is probably a huge target, people would attempt to shoot at it even with small arms, and it is not impossible to get lucky with them (happened at least once in Iraq War for example, when a random farmer downed a US helicopter right on the start of the war with his hunting rifle... the chance of it working was tiny, the rifle didn't even had the range to ever reach the helicopter, but somehow, it did...)
You can infer something from phrases like "flying super heavy cargos" and "by bringing infrastructure ... that are normally too big for airlift" but it would be interesting to see if anyone has something to add directly on that topic as to what exactly the drawbacks to that scale are. The fact that only one was ever made also implies that the uses are limited.
So by those rough guesses, the AN-225 should be ok.
That said, the moment you have a too heavy, or too big load for an AN-124, then the extra fuel cost of the AN-225 has almost infinite value.
The drawbacks to scale always have to do with complexity, and ground infrastructure. The AN-225 can't operate from as wide a variety of fields that the AN-124 can (though this shouldn't be a huge concern from commercial use).
Structurally, the modifications from the AN-124 to AN-225 aren't super complex. They basically added plugs before and after the wings to extend the fuselage, and added a wing extension. While these aren't trivial changes to an aircraft, they're basically the simplest type of structural change you can make. Oh, I guess there's a tail modification, but that's not that risky either.
I mean I guess the point is that you probaly would not want a whole-scale replacement of AN-124 class lifters with AN-225, but keeping a few around enables entire types of lifts (and therefore operations) that simply aren't possible. The key would be to estimate what the appropriate amount of AN-225 are.
For an example, the famous Beluga Airbus enables a form of manufacturing distribution (for good or for bad) that simply isn't possible without it existing. You would never want a giant fleet of Beluga, but having it is invaluable.
Take the following paragraph, for example:
> For China, the An-225 would open whole new frontiers in commercial and military air transportation. A fleet of civilian An-225s could quickly ship heavy and bulky cargoes of massive scale, ranging from construction equipment to consumer goods. For humanitarian purposes, the An-225 could support disaster relief operations, able to fly in not just large amounts of aid, but also by bringing infrastructure like power generation and water treatment that are normally too big for airlift.
That spells out in plain language why possession of the An-225 and its technologies make economic sense for China. And the paragraph after that state the military reasons why China would need the An-225.