As the pretty green letters next to my name suggest, I know a fair bit about the Roman army. Recently, I've been trying to expand that knowledge a bit onwards and upwards, so to say, and started to read Eric McGreer's Sowing the Dragon's Teeth, a rather excellent work that combines translations of some 10th century Byzantine military manuals with quite a bit of analysis.
One thing that surprised me as I read the first manual —emperor Nikephoros Phokas' text known nowadays as the Praecepta Militaria — is the instruction for the cataphract charge.
The text states quite clearly that these extremely heavily armoured cavalry are supposed to form up into a blunt nosed wedge formation and
move in proper formation at a trotting pace and smash into the position of the enemy commander
Was that normal in Byzantine warfare? Do other sources confirm this, and do modern historians believe their testimony?
There doesn't appear to have been a consistent agreement on how the attack was made.
The earliest account is Maurice's Strategikon (tr. George T. Dennis, very late 6th century) which states that, in close order, "they ride on in good order, not too fast but at a trot, to avoid having the impetus of their charge break up their ranks before before coming to blows with the enemy, which is a real risk" (P38). P39 says that galloping is for pursuing the enemy in open order. However, pursuit might also happen in close order, with the implication that this would also be at a trot.
There's then a break in the tradition of military manuals until the 9th century Peri strategikes ("The Anonymous Byzantine Treatise on Strategy", Three Byzantine Military Treatises, tr. George T. Dennis), which states that "it too possesses its own kind of forcefulness in attacking, since it does not fall upon the enemy in a slow or measured way but charges at full speed. This is terrifying to men who have not had years of combat experience".
Next comes the late 9th/early 10th century Taktika of Leo VI, which states that "they advance in good order, not too fast but at a canter, a measured gait, the so-called kalpa, so that the impetus of their charge might not break up their ranks before coming to blows with the enemy, a very risky action." (The Taktika of Leo VI, tr. George T. Dennis, P117).
Following this, composed in the first half of the tenth century, is the Sylloge Tacticorum (A Tenth-Century Byzantine Military Manual: The Sylloge Tacticorum, tr. Georgios Chatzelis and Jonathan Harris). This doesn't give us a speed, just that "the triangular will immediately advance against the enemy with an undoubtedly irresistible charge". (P102)
The Praecepta militaria, as you've noted, mentions that "the front of the triangular formation must move in proper formation at a trotting pace and smash into the position of the enemy commander" (Sowing the Dragon's Teeth, tr. Eric McGeer, p47), and the Taktika of Nikephoros Ouranos (ibid, p129) merely says that "The triangular formation of the kataphraktoi must then carry on at its pace and its front line must strike against the commander of the enemy formation."
There might be more, but these are the sources I have to hand. One problem with this is that Leo probably never went to war, and his passage is almost a verbatim quotation of Maurice, so it's not easy to tell whether or not the advice on the cavalry charging only at a trot reflects actual practice or is what he thought should be done. Leo quotes also Maurice regarding the armour for cavalry without any significant modification, whereas the Peri strategikes includes felt helmets, thick padding under the armour and the addition of lamellar armour (P55-59) and is probably more reflective of military practice overall.
The Sylloge Tacticorum is little help, because it's ambiguous enough that it could be interpreted either way. While it draws on the Taktika of Leo, it also updates the armour in a similar manner to the Peri strategikes (but with more variations in armour materials and types) and is a transitional text, introducing increased specialisation among the soldiers and cavalry, but with the kataphraktoi still primarily relying on lances rather than maces.
The role of the kataphraktoi in Nikephoros II Phokas' manuals appears to have been to use the bulk and armour of their horses to push through the pikes of their opponents and get in close enough for their iron maces to batter down any shields or heavily armoured infantrymen. By advancing purely at a trot, they maintain a very compact and orderly body but also have enough momentum to not be easily stopped by pikes. This would allow them to be intimidating and create the biggest simultaneous impact possible but also still reach their enemies if they didn't turn and run.
According to John Haldon (Warfare, State and Society in the Byzantine World 560-1204, P198-199), there was a decline in infantry quality soon after Maurice, and it wasn't until Basil I that serious attempts were made at strengthening it. The result is probably that a rapid cavalry charge, even if it was not as orderly as a slower one, was very effective against the infantry they were expected to face. As the quality, equipment and training of infantry improved, it became more difficult to rout infantry through the threat of a charge alone and, as a result, there was a change towards using very heavy cavalry to try and physically break apart the infantry by hitting them in a focus spot, getting in past the pikes and engaging them at close quarters.