Boris Gudenuf
Deity
Because I believe the Byzantines should at least get the Dromons first. Second, I would give them the Varangian Guard.
If they were to be a UU give them to the Sarmatians.
You are right in that they weren't used by everyone. But if they were used by more than two, maybe three different groups of people, I don't think that should make them a unique unit to one particular civilization.
I mean if we can have Knights as a general unit, and they were less widespread than Cataphracts, I don't see why Cataphracts couldn't just be an upgrade from them? This is assuming that Knights would also use similar resources such as horses/iron, unless we radically change the way units are produced.
Knights, however, were a general unit: armored men with lances on horseback (and occasionally adding bows as well) were a feature of European, central Asian, Middle Eastern, North African, and Tang China armies from the late Classical to the Medieval or Renaissance with various types of armor and degrees of 'professionalism' and Unit training. There's a reason besides familiarity that they have been a standard unit since Civ 2 (or before: I never played the original Civ) and have spawned a bunch of replacement Uniques from Civs all over Eurasia.
I believe, though, that Cataphracts fall Inbetween: too general to be Unique to a single Civ, but not general enough to be a 'standard' unit. I believe this puts them potentially into an entirely new 'class' of units, and that's another thing that could possibly be explored: units that require something Special to be acquired and built so that they aren't general, but are also not limited to a single Civ. And other examples of such (potential) units: Dreadnaught Battleships and Medium Tanks (Civ's 'Tank' unit) were both only designed and built in their respective starting Eras by only about 10% of the countries in the world, because they both required a combination of massive Industrial Production and multi-line research and development that simply were not generally available to everybody thsat wanted them (Note the numbers of countries that 'bought' American or British medium tanks rather than develop their own in the 1950s and early 1960s).
In other words, Cataphracts are not necessarily completely Unique, but could be an early example of a type of Unit that requires either a peculiar combination of circumstances or a serious commitment to acquire.