Quote Originally Posted by Martin Greywolf View Post
The sole advantage of chariots is that the riders are harder to hit - they are in cover, provided by their horses, and even if you shoot the horse, it will not usually fall straight down and crash the thing, it will start to slow down and die.
You and others (including the one asking the question) have touched on the other advantage, which is worth calling out explicitly - you can do charioteering with animals that are not functional as cavalry mounts. Early horses which are too small to ride, fantasy animals that are anatomically inappropriate or dangerous to ride, etc. Attaching a vehicle broadens the animal-powered-mobility-in-warfare possibilities by quite a lot.

(Not to say that the advantage of cover is negligible either - while it's not a chariot, we can take the Hussite war wagons of the 1400s for an example at the other end of the pre-modern tech tree that focuses more on the cover angle you're mentioning. )