The issue would be "no casualties" element. What other unit type can reasonably expect to take no casualties in a large battle. As written every realm would simply make sure to take Horse Archer elements, which would then end up in some running duel with each other.
In RL Horse Archers would come under attack from the enemies archers. Their fast movement made them hard to hit, but then the return fire also caused them issues, as they had to maintain speed to avoid it, which affected their own aim.
Its not a serious suggestion, just thought it'd be cool to have a single unit of them. If they were freely available it'd be very bad for game balance.