The chariot came about because of the size of the average horse. The horses of the time were similar in size to Welsh ponies.
The first fighting vehicles were four wheeled carts with four side rails. Hard to turn, hard to clamber out of the box and heavy.
Then came the chariot. Three-sided box on two wheels. Two horses, much faster, much easier to turn.
The chariot morphed into a more rounded (but not round) front with side panels that sloped down in the back, making dismounting and remounting much easier.
The Battle of Kadesh was the largest chariot battle...
https://en.wikipedia.org/wiki/Battle_of_Kadesh
The Egyptians and the Hittites used their chariots a bit differently. Egyptians had a driver and an archer. There was a quiver on every corner and the archer would work around the driver, to get his best shots.
The Hittites used a little heavier chariot, with a driver and an armored spearman. Sometimes, they'd add a third man to the chariot, armed with a sword.
Once calvary came about, goodbye chariots...