[Action]

The Tien Chi medium horse archers with

14 prot
11 morale
12 defense
10 str
10 Attack
3/23 move

Light Lance/Hoof/Composite Bow/Buckler
for 35 gp 21 resources

seem like they might be useful, in small numbers anyway. For example, you can place them in front of your normal archers or commanders to protect them from melee a bit, since they will just stay in place and shoot rather than charging forward.

I haven't tried these particular units but the Bakemono Samurai Archers with longbow and no-dashi are nice for that multi purpose role.

I think medium cavalry could be made pretty useful in small numbers if they eliminated the -2 precision penalty.

True light cavalry will probably always be pointless due to the nature of the battle engine. Giving them surival for every terrain and less supply need (small steppe ponies can just graze unlike warhorses) would be a good start though, along with the +2 precision.