Military reforms can happen for political and economic reasons, as described above. Or they can happen for military reasons.
The usual military reasons are:
1. Absorbing a huge source of foreign manpower into your army that isn't culturally suited to fighting the same way your own people do. As with Alexander's Macedonia (later Seleucid empire) conquering the Persian empire and having to employ eastern troops, some of whom the Greeks have to let fight according to their own traditions and skills - light missile cavalry and archers instead of heavy infantry, for example.
2. Getting your butt severely kicked in a very large and important battle by an opponent fighting in an unfamiliar way that your current military methods are not suited to countering. E.g. Rome having to abandon the Greek-style hoplite phalanx after being thoroughly trounced by the Gauls at the Battle of Allia (resulting in the sack of Rome, which really did become 'Barbaropolis' for a while!) This resulted in the Camillan reforms, creation of new heavy infantry, Hastati and Principes, equipped more like Gauls with oval shield instead of round Greek aspis, and javelins for throwing before the hand to hand fighting begins. Principes equipped with Gallic-style chainmail armour. Helmet based on Gallic design.
If the KH ended up dominating most of Europe using their existing military system, why would they need a military reform? However, if they got their butts kicked in a critical battle by Gallic or Germanic barbarians, they might start thinking about modifying their system beyond simply recruiting local barbarians into their own armies (Galatians, for example.) Mind you, the KH actually have a very wide variety of units at their disposal anyway, including updated hoplites (they aren't stuck with the old classical ones) and they should be able to tailor their army to meet almost any threat. Only Scythian and Pahlavan horse archers pose a serious problem, as they did for Rome. To which the KH can only recruit local horse archers or hire mercenaries.
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