: I may be missing something blindingly obvious, but this
: should answer your questions.
I think it was an expense/time consideration for Bungie. It costs quite a bit to render something like that into sprites, and they were working on a pretty inflexible deadline if I remember correctly.
Plus, real cavalry charges through enemies, and does not stop to stab with a lance (like the beautiful Hexographica cavalry units did, rendered by hexo's chief unitmaker Re-Animator). Myther William Wallet, when he created his horseman unit for Freedom II, also had the same limitation: the horse stops running and the rider swings his sword.
More realistically, a unitmaker would have to script a constantly detonating projectile to closely follow the charging horseman unit. This would take time that Bungie probably could not spare.
Clearly there are horses in the story, though.