Cavalry is mobile on the battlefield, not in travel. Funny fact: Humans are faster at overland travel than horses. While horses have a higher maximum speed, they can't maintain it for long and need more rest. With armies you also have the whole baggage train thing - you need to move more than just the soldiers.
I actually believe that cavalry is simulated a lot more realistically in BM than in most other games.
Yup, that is why on theory on early human hunting basically has us running things to death.