How do you figure their equipment lists are the same? Magewrights exist to make "common magical items" and that doesn't exist in the other settings.
Sure, you have a wizard's college, and maybe a few apprentice wizards might make something, but there is no where near the production capability to outfit entire armies with magical gear, which Eberron traditionally has.
And while Iuz does exist, he doesn't exactly take the field himself, he sends his minions to do the fighting. He fields armies. And that is because of how difficult it is to fight an entire army by yourself.
I would also like to note, that the Houses of Eberron (while fractious) can and do cooperate, and do so at a macro-economic level. So, their betrayals of each other take place in the world's of economics or corporate espionage.
Meanwhile, the fractious archcasters in the other worlds are in direct opposition on a personal level, and even if an Eberron army couldn't take out a archcaster (something I highly doubt to be true unless you used 3.5 rules which made high level characters immune to low level ones, which would not exactly be accurate fiction) there is little to prevent the enemies of that caster from showing up and killing them after they used all their mojo killing an army.
To focus on some more tactical discussions.
Summoning Elemental Hordes: Elementals are not immune to normal attacks, and they are not resistant to magic. They are tough, but nothing to suggest they are tougher than mage-bred creatures or Warforged Titans.
Banshee Wail isn't 5e, so I can't comment, but if it just kills people within 60 ft who fail a save... That actually isn't terribly devastating compared to an artillery blast, and 60 ft in a loose formation is not many people of an army, who could then turn and fire upon you.
Cloudkill: Eberron is meant to emulate some of the horrors of the World Wars, so gas attacks would be common. Add that to the fact that Cloudkill moves at a horrifically slow 10 ft a turn, anyone not caught in the tiny 20ft radius area (compared to the size of, again, an army) could easily avoid it without even having to dash, and again, focus fire on the caster.
And, one size for a moment, I'm going to pull some British empire numbers just for a quick glance through.
A single Company of men was generally about 220. They generally stood about 4 lines deep, that is 55 men to a line. If I was dealing with artillery/fireballs, I would generally want to space about 10 ft apart. Everyone has a weapon capable of long range after all, so formation fighting would generally be more of a detriment than an aid.
So, at 10 ft apart, the first line would stretch nearly 550 ft and be 40 ft deep. An area of 22,000 sq ft. Even a truly massive spell with a radius of 50 ft will only cover 7,850 sq ft. If that kills everyone in it, you still have about 150 soldiers left.
And armies are generally multiple companies.
Okay, part of the problem here is that this is a Spelljammer discussion, which moves us to the common element of 1-3e, where SPelljammer exists. Eberron is also fundamentally and originally a 3e world.
Money and equipmentwise, eberron and the other worlds all use the same price lists, and the same wealth by level. It's all part of the rules. They have no advantage whatsoever in equipping anyone. Magewrights exist to make magitech to increase the standard of living, and have absolutely no macro influence on WBL and what can and cannot be given to your soldiers. If you are going to start claiming that Eberron can make things that Faerun cannot, the obverse also applies. Faerun has a far, far deeper magical heritage then Eberron can imagine, and again, Archcasters all over the damn place.
Look up the area of effects for Transmute Rock to Mud and Cloudkill in prior Editions. They are freaking massive, and Cloudkill moves at 30 there, not 10. If you are trying to hold a position, you are dead. It instantly kills anything of 4 HD or less, 5-6 HD saves at -4, 7-8 at normal, and 9+ are immune. So the archcaster can fill the area around him with death and be completely immune to it.
Oh, and then Widen it to double all the dimensions, too. And make it invisible, potentially.
Here's the stats for a Warforged Titan: Warforged Titan - Eberron Unlimited
Here's Elemental Swarm: Elemental Swarm :: d20srd.org
Here's the elementals: Elemental :: d20srd.org
A huge elemental will slaughter a warforged titan, and a Greater Elemental will kill multiples of them. If a Titan dies, you are out massive amounts of resources used to make it. If an Elemental dies... the archcaster casts the spell again.
a Lightning BOlt has a range of Long. It can rip a 10' line 1200 feet long through a formation.
Greater Lightning Storm can call down literally dozens of bolts over time onto a scattered formation, completely disrupting any unit cohesion.
Summon Monster VI+ can Summon tons of low level monsters right on top of you.
That save to avoid Wail of the Banshee is likely to be a 29. A soldier might have a 5% chance of saving against it.
A Meteor Swarm can take out half an acre, which means the core of your elite troops, or your command center, from 400 yards away or up in the air.
A Gate spell could bring in a Planetar, another 17th level caster.
Holy Word spells will instantly kill anyone of the wrong alignment and half the level or less nearby.
Those are just AoE's. An archcaster's ability to take out single, expensive targets is naturally much higher. One disintegrate spell can take out a Warforged Titan. A rain of fireballs and lightning bolts, or Just Call Lightning, from up in the sky will obliterate your artillery. Command of the weather will drown your troops in water and mud and leave them unable to go anywhere. Call in demons or the like to spread disease among your troops. Charm their commanders to give them the wrong orders.
I am not an Intellect 30 Archmage. Such beingsa re Not Dumb. Low level people have no way of dealing with everything an archcaster can bring to the table repeatedly.
The game is not the real world. In the real world, you shoot somebody, anybody, they can die instantly. In D&D, you can empty the entire clip into a high level character, and they'll just look at you funny. The combination of HP and AC is basically untouchable in the game we are talking about.
Now, if you want to go 5e... they reined in things a lot. But 5e is not the game of SPelljammer, nor the game Eberron was designed as. The bounded accuracy is not a thing. High level existences can kill armies on their own, bring down nations and kings.
Iuz doesn't move from his capitol because that's where he's strong and his defenses are. If he moves outside it, his enemies could act, and take him out. Those high level foes can't act freely either, because if they get distracted, Iuz could do something.
High levels constrain high levels. Eberron does not have those high level characters. It's part of the canon, the very design of the setting, that it NOT have them. It's the PC's who will end up being those high level characters, there's no Elminister to pull the world's fat out of the fire.
Faerun, on the other hand, is overflowing with archcasters, and is a setting for high level characters and high magic. Eberron is not its equal in raw power, and it is DESIGNED to be that way.
Yeah, you can buy a better pair of shoes and take the lightning rail. But that doesn't make you tougher or more deadly.