It does seem dumb that LH can't catch LF from 2 Hexes away

Regarding chasing routing units... I think the troop quality, drill factor, number of routing units nearby, presence of a commander and his level should affect the chances of persuing. e.g.
1. Elite, Drilled units, next to Alexander (or Alexander himself) would almost never chase a routing unit unless a lot of the nearby enemy are already routing (I figure that either they'd want to kill them, or ensure they don't rally).
2. Poor undrilled units, out of control of commanders may well chase. History is littered with examples of poor, or weakly led, units throwing away a good position by chasing a (real or feigned) 'routing' enemy.
All that needs doing is to turn these factors into a percentage chance

What would be nice is to be able to move that would simulate a rout. i.e. move into contact range then when hit the unit 'routs' to a predefined point. This would add a new dimension to tactics for the game. In counterbalance, there should be a small chance (that increases with troop quality, discipline, nearby comander and level of commander) that the 'rout' is actually believed by some of the same sides troops and thus creating a real rout!

Finally, I also agree that undrilled cavalry are really slow to turn and it restricts their effectiveness.