The chariots are actually great rout chasers, but not independently. I will usually send the chariots after the fleeing enemies, being careful to choose the faster troops first (I've caught cavalry with chariots, even through wooded areas. Are chariots naturally faster than plain ol' horses?), then send the faster foot troops (slinger/woad warriors) after them as well. The chariots, if you plan it well, will run through the fleeing troops, killing some and knocking the rest down, hopefully through multiple units. Your fast troops will catch up pretty quickly when the enemy are lying on their backs, and you'll have few problems wiping everything out.

Other than that, missile-less chariots are best used as shock troops, I find. Charge your opponents from behind with them and run them over, then pull them out and do it again. Even the mere presence of them is enough to screw around with the enemy's morale, so it's not really a bad idea to have them close, even if you're apprehensive about their actual combat ability.