You'd also need to explain how they got the undead beasts to accept them in the first place without them getting bucked off/eaten. Ghouls are not undead in the way that Skeletons are. In the case of a Black Knight, for example, both rider and mount are summoned from the dead and so would both follow the Necromancer/Vampire's lead, whereas with a Ghoul cavalry unit you're pairing a living Ghoul with a steed risen from the dead by the Ghoul commander, so the steeds would need supervision by the Ghoul leader. True, you have Ghoul characters riding Zombie Dragons and Terrorgheists, but those are being ridden by the Ghoul King himself and are thus easier for him to command, whereas these lesser cavalry steeds are being ridden by Ghouls with no magical power and are thus less easy to control by the Ghoul King, potentially resulting in them running amok or falling apart if they and their Ghoul riders stray beyond his locus of control.
Sounds pedantic, doesn't it? But I'm only mimicking your own attitude toward Fyreslayers - you can't force one army to follow one rule (which GW tends to ignore anyway), while giving all the others a free pass because you like them more.
I mean, having them only be able to control their mounts while within their king's domain (or at least area of influence if the king goes on the warpath) would be perfectly in line with how the FEC work, and thus be completly acceptable. It's not like FEC really roam all that far from their established domains. So that's not really a issue, nor is it pedantic.
Alternativly, just make the cavalry lesser nobility, who have enough magic to command a lesser steed.
Or as a final option, simply state that when a kingdom falls to the vampiric curse everything is afflicted, including their mounts and beasts of burden. So the insane ghouls are riding on equally insane ghoul horses.
All three options are perfectly in line with established FEC lore.
It's pretty obvious they already have beastmasters in order to successfully raise and tame Magmadroths in the first place, it would not be much of an extension to say those same beastmasters could raise other creatures in the vaults of the Magmaholds equally successfully.
Seraphon, CoS (or well, the old ones at least, not sure how significant the dark elves are in the new version), Skaven, Idoneth, Ogors, and probably some others I'm currently forgetting, are established as beastmasters who regularly raise or capture various types of beasts of various purposes.
Fyreslayers on the other hand are only ever shown to interact with Magmadroths.
An interaction that is based specificly on the fact that their god and godlike ancestor did battle resulting in a link between the two species.
Which is why they don't raise anything else, because there is no other creature which with they have this kind of link, and they do not have a beastmaster type culture.
And yes, this can be expanded upon,
but then they'd need to actually expand things and explain why they started raising other beasts.
As it currently stands, the Fyreslayers have no equivalent to say, dark elf beastmasters, whose job is specificly to raise various types of beasts. They just have the magical link that was created when Grimnir fought Vulcatrix which some powerfull fyreslayers can use to train their own Magmadroth.
Similarly, the ideas I mentioned of animated Slayer statues, wheeled shrines to Grimnir, units of Priests and female warriors are all very much possible with the existing lore and would need just a couple of lines of explanation.
Slayer statues are the easiest to make work, as animated dwarven statues have actually appeared in lore here and there.
Any sort of siege equipment/wheeled statues/etc. would feel massivly out of place as they don't have any history of doing this.
Sure, you can say they changed their mind, but you'll have to explain why an army that previously fought with no warmachines whatsoever is suddenly dragging all sorts of nonsense to the battlefield.
As for units of priests & female warriors; both of those are just more angry naked dwarfs and doesn't really fix the lack of unit variety. But sure, you could add them.
Er... they made it?
They have guns that can fire lava as a projectile weapon, that's a significant piece of technology. Someone had to invent that, and if they could create that they could create other things. The old Slayer army list from Warhammer Fantasy included the option of a Slayer engineer character called Malakai Makaisson, it wouldn't be much of a development to include another caste of Fyreslayer society dedicated to building, repairing and maintaining Fyresteel weapons. Perhaps they're combi-smith-architects who also design Magmaholds before they are built, and are more focussed on maintaining the old, very much as the Fyreslayer army as a whole does, rather than experimenting with the new like the Kharadron do.
I'm not saying they're completly incapable of making the things. They're good enough blacksmiths that they can make a chariot or something. Not like a chariot is all that complicated.
However, they have no history of using any sort of equipment in war. Hell they don't even use siege equipment, they just use magmadroths to batter down a wall if they need to.
Nor do they have a history of being inventive.
Which makes adding any warmachines, however minor, feel immeadiatly out of place cuz it's completly out of character.
The new war machines introduced into the army could have been as old as the hills, and just kept in mothballs in the deepest vaults until the time was dire enough to get them out again.
I mean, you'd think they'd have used those at some point during the millenia against chaos when hold after hold got destroyed. It'd be completly nonsensical to pull out something as basic as a chariot right now.
Which is kind of the core issue fyreslayers suffer from, their initial characterization has been so absurdly limited, that at this point adding new stuff is going to result in a bunch of things retro-activly looking rather dumb. Again, GW massivly wasted their potential on the intial release, and then doubled down on it by releasing bits of lore further cementing this waste. At this point fyreslayers need some actual work to allow for sensible expansions of the army.
It wouldn't be similar to those updates at all, both of those updates are actively replacing old models with new ones (and I severely doubt GW have gone to any great length to explain in-lore why Cold Ones were replaced with dull-generic-Jurassic-World-velociraptors, how Razordons went extinct or why Cities of Sigmar have completely changed their uniforms all of a sudden).
CoS already had wildly varying uniforms and combat doctrines that differed per city, as well as evolved over time depending on the enemies they faced. So they don't need much more explenation than "Some General introduced a new standard uniform and some new doctrines"
Seraphon have an established section of beastmasters utilizing various different beasts, so replacing one beast of war with another is perfectly fine. The implication being this new beast of war is better/stronger/easier to raise/etc.
A Fyreslayer expansion, on the other hand, would be just another second wave release like those Lumineth, Slaanesh and Sylvaneth got, that would organically expand the army from the original roots of the first release. GW never needed to explain in great detail why Lumineth suddenly got to ride kangaroos or Sylvaneth got to fly around on giant insects (other than "iT's aElVes So wE thInK it'S CoOl"), and they would not need to do so with a Fyreslayer expansion either.
Riding a random forest creature doesn't really need much explenation for the literal spirits of the forest that are sylvaneth.
Lumineth have been established from the start as having a massive empire with all sorts of different nonsense and the first wave of Lumineth where very explicitly only a small part of this empire.
I don't really like any of the elves, but their initial characterization left plenty of room for their 2nd waves, as well as for any futher 3th or 4th wave.
In contrast; when the fyreslayers where established GW immeadiatly wrote themselves into a corner by making them consist of literally only angry naked dwarfs, giving them no war machines, and limiting them to 1 animal companion which they only use because of a divine link between them and this animal. And since their release, GW has doubled down on those limitations by consistently depicting Fyreslayers in this limited way.
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You know very well that I like Kharadron just as much as Fyreslayers, I was just using that generalisation to demonstrate how narrow-minded
@Canas' attitude to the Fyreslayer army is. He (and you as well to a lesser extent) seem to be trapped in this nonsensical mindset that the Fyreslayer army has to be kept in a particular description box while other armies don't need to. Probably because neither of you like the army and are quite happy for it to fail.
Honestly, I like fire-themed dwarfs. Fyreslayers is just a massive waste of potential due how absurdly limited their initial characterization was, and due to GW continuously doubling down on this limited characterization and refusing to add anything novel to their culture.
And yes it can be fixed, but it'll require some retcons and general adjustments to their core characterization if you want it to feel natural.