Couple Roman military history questions for you. What advantage did the Roman gladius and shield wall have over the Macedonia phalanx that predates it? And, why didn’t the Romans ever train their own cavalry and archers on a large scale, preferring to rely on foreign mercenaries? It seems to me that a loyal cavalry force especially would have come in handy in dealing with the barbarian invasions.

Question 1: Romans vs. Macedonians

Chiefly, flexibility. Because phalanxes fought shoulder-to-shoulder in deep ranks, they were rather slow to move, especially laterally; this meant that they were vulnerable to being flanked. By contrast, the Roman maniple system, being much looser and more decentralized, could respond rapidly to new developments.

This difference was famously worked out at the Battle of Cynocephalae, where the Roman legions initially struggled against the weight of the Macedonian phalanx on the left, but the Romans were able to quickly move twenty maniples to take advantage of the withdrawl of the Macedonians on the right and attack the Macedonians from the flank and the rear, causing a complete panic that shredded the phalanx.

Question 2: Roman Cavalry

I think this has to be understood as a matter of opportunity costs. Training good cavalry takes many years training and a not-inconsiderable amount of resources in terms of horseflesh, so you tend to see premodern societies choosing whether to invest their time and resources into cavalry or infantry. (Same principle goes for archers, btw.)

Since the Romans had primarily an infantry culture, it was much more efficient to hire allied cavalry when and if they were needed and rely instead on their infantry to win the day. 

Now this did change over time as the Roman Empire’s borders stretched and came under pressure from horse-riding tribes from outside the Empire, which made the cavalry’s rapid response capabilities more important.