My guess it that civilisations that existed in ancient times were much more isolated from each other and, therefore, their military practices evolved separately and uniquely. This is why in early periods, armies had rather different types of troop.

You can also see what happens when one civilisation spreads its culture -- following Alexander's campaign, other countries started using some kind of phalanx.

By the 18th century, European countries were much less isolated. Due to the cultural ties, their military started looking similar to each other.

Take Peter the Great, for example. His reform of the Russian army was influenced by the Prussian military. He even dressed them similarly.