Chinese Mounted Archer - How to break original AOM concept?

The original AOM concept was that every unit has one main unittype:

• Atlantean Turma is an archer. Counter it with counter archer units.
• Egyptian Chariot Archer is an archer. Counter it with counter archer units.

Rule: NEVER GIVE TWO MAIN UNITTYPE TO AN UNIT.

but

• Chinese Mounted archer is both an archer and a cavalry, which means: counter it with counter archer units OR counter cavalry units. It has two times more counter than Atlantean Turma or Egyptian Chariot Archer. Every second unit can counter it.
• Example: you have an Atlantean oppenent. Chariot Archer can be countered by Turmas. Mounted Archer can be countered by Turma, Katapeltes and Fanatic.
• After all chinese have 5 cavalry units: Cataphract, Scout Cavalry, Mounted Archer, War Chariot and General. Atlanteans have one: Contarius. Great! I don't think it was a wise decision to make Mounted Archer a cavalry.