An important thing to note is that historically, the difference between light and heavy cavalries was more often than not a result of different socioeconomic backgrounds. Light cavalry tradition tends to come from societies that are more rural, more militia-heavy, with less manorialism but more pastoralism, or just outright nomadic (such as the Mongols).
There is a reason why many states and empires throughout history tend to recruit their light cavalries from a particular ethnic group (Uhlans, Hakkapeliittas, Croats, Akinjis, and most famously, Cossacks).
As a result, a simple combat-role-based division of "light" and "heavy" cavalries in a game will always feel awkward from certain angles, as the game did not really try to model the underlying factors that produced these troops (which is not a criticism - a game has its own priorities).
(BTW, the same was true for light infantry; the Cretan light infantry of the Classical Mediterranean and the French Zouave units are famous examples.)
I don't know of any computer game at any scale that has effectively modeled the Societal aspects of the military.
"Every military force reflects the society that produced it."
More specifically, several states, including Mithradates of Pontus, tried to build their own Roman Legions, and all failed. It's not enough to equip a bunch of men with swords and full body armor and shields, they also have to be trained and maintained and, most important, motivated to fight. Most of them never got as far as being able to afford the training and maintaining, and men not trained or paid are notoriously hard to motivate.
In Civ VII (or any Civ, for that matter) terms, that means there are some types of troops that require you to change your Civ, sometimes significantly, to get and keep them.
Both light cavalry and light infantry (in the classical west, frequently missile troops) were socially below the 'real' close combat fighting troops - this, more than any question of weapons' effectiveness, is why massed archers or slingers never became popular in classical Greece or Rome: they were bound to be recruited from the lowest economic class, that could not afford to provide weapons and armor for themselves and take their place in the line of battle, like the hoplites and early Legion infantry.
And some weapons systems required such concentrated and prolonged attention to master that they were always going to come from specific parts of a society or particular societies. Prime example is the Horse Archer, which required both continuous access to horses and the time to learn how to both ride and shoot. Quite simply, it was not possible for any set of city dwellers to have the time, money and space to learn and practice these skills. Consequently, every army that included horse archers was either from a pastoral culture or hired them from a pastoral culture: Scythians were hired by Alexander and other Greek states and Persia, Huns by the Roman and Byzantine Empires - no militarily-significant number of Romans ever tried to learn how to be horse archers: it was far, far cheaper and easier to hire them.
Lesser known specialists were the Cretan and Rhodian slingers, who were hired by everyone who could get them, because they were life-long practioners with the sling and, as professional slingers, were first to fire streamlined lead 'bullets' with much higher velocity than rocks. They could outrange archers and knock someone sprawling even through armor: a pellet hitting a helmet literally rang the soldier's bell and concussed him.
Including a Society mechanic to obtain certain types of troops in any number would be more accurate (for whatever that's worth) but also restrict player choices in ways never done before to my knowledge, so would probably be a hard sell. On the other hand, Uniques in the form of 'special recruits' like tghe slingers and horse archers could only be available from certain Minor States and therefore have to be hired, which would at least be a start.
