I'm all in favor of giving more riders the charger knight treatment. unless the beast is the main unit it shouldnt be one. for example fist of bastion should just be a barb.
I like the Age of Wonders system where all mounted units are recognized as such. Pox already has an analog in flying units and some abilities granting bonuses or penalties when attacking flying or nonflying. "Mounted" would be more of a class than race here though.
nearly all of the other mounted IS units have race beast, it makes no sense that charger knight doesn't
Race focussed bgs tend to get out of control when chamos receive multiple races for little to no reason. Especially rider champs.