Up until that point horses could be harnessed to pull wagons or chariots, and were often ridden *to* a battle, but not into one. Without the stability in the saddle that the stirrup provided, fighting from horseback, whether with sword or spear, or with a horse bow (shortbow, in D&D terms) just wasn't practical. You threw yourself off half the time.
Oddly, the stirrup was invented and used, then forgotten for a century or three before being reintroduced.
As for accuracy from a speeding chariot: The PBS special I saw showed a man shooting at man-shaped targets as he passed. He was scoring head shots with pretty much every shot. And the ground they were driving over wasn't smooth and clear either. It was hard scrub, with sandy stretches that could easily bog down a wheel. The narrator commented on the concerns about the rough ground.
Now I personally find it hard to explain how the horses would survive such a charge, since they're out in front and unprotected. It's like asking opponents to pincushion them. You take one horse and you've stopped the entire chariot. Perhaps it was considered "cheating".
In any case, while the chariot had no suspension to speak of, the platform, woven from strips of raw hide, at least provided a cushioned platform for the riders.
Chariots played a part in the Boudicca Rebellion in Britain as well, when the locals rose up against Roman rule. They too used speeding chariots to make what were essentially strafing runs against their enemies. This proved less than effective against a hardened and tight Roman formation, however, when the men had their shields all but locked together. That was as late as 61 A.D..
Since the stirrup didn't come into broad European use until the 5th or 6th century AD, the chariot was still a useful weapon of war. The Roman's standardized the wheel base, which was reflected in many of their roads. (Full "High Roads" were all stone. Many lesser tracks however consisted of two stone tracks spaced for the chariot wheels, with a earth strip in the center.) This standardized with, in fact, helped encourage a similar standard in wagon wheel spacing for centuries to come, and was carried over into automobile wheel base and the spacing of railroad rails. (The first railroad wheels were made using the same jigs that had been used to build carriage wheel sets, so they had the same spacing.)
So echoes of this ancient vehicle/engine of war continue to this day. There's a horrible joke that carries this one stage further: The size of the solid fuel boosters used in the space shuttle and other orbital vehicles is limited by the size of a train flatcar used to carry them. The flatcar size is based on the width of the tracks. The width of the tracks is based on the width of horse drawn carriages. The carriages width is based on the old Roman roads. The width of the roads was set by the width of a Roman chariot. The width of a chariot was set by the width of two horses side by side that drew the chariots.
So if it ever seems that crucial decisions at NASA were decided by some horses ass, you now know which horses ass to blame: The Romans!
ncG1vNJzZmivp6x7prrWqKmlnF6kv6h706GpnpmUqHyzwcueqmappZrAtbXOp2Shp6dixLDBy51ksqelYrWiusOlZJplk52us7XOrWVsbmhtgHZ7