: 6) The roman cavalry was low quality? that's news to me,
: because the cataphracts of the Byzantine Empire were
: quite good cavalry
Well, for one thing, Roman cavaly's effectiveness was limited by the fact that they didn't have any stirrups, but it goes deeper than that. The Romans never seem to have really figured out how to use cavalry effectively, and Roman cavalry seems to have been much less effective than their equipment and numbers would suggest. In fact, during the Second Punic War, Roman Heavy Cavalry units were routinely trounced by smaller numbers of Hasdrubal's Numidian Light Cavalry, which frequently led to the Roman flanks giving way, and so causing some of the greatest Carthaginian victories of the war (such as at Cannae, where such tactics destroyed the largest army Rome had ever fielded up to that point: 8 double Legions; nearly 80,000 men.)
I'm not that knowledgeable about the Byzantines, but Late Roman cataphracts possessed too much heavy armour to be able to charge and still remain in formation. In fact, they usually trotted into battle with lances levelled, rather than doing true charges, and perhaps it would be more accurate to think of them as a kind of mounted phalanx rather than as shock cavalry. All this meant that, while a cataphract unit was difficult to break, it was also not very manoeuverable, which a cavalry unit really needed to be, since flank attacks were the main method by which cavalry cound even the odds against opposing infantry blocks. The Romans never seem to have been able to produce shock cavalry as effective and well trained as Alexander's Companions, for example.
