For China, the replacement was both functional and economic. Competent cavalry, which could also be used as shock cavalry, proved to be much more effective than chariots. It still took about two hundred years for the chariot to totally disappear. But that might partially be a problem of terminology in texts and conservativism in pictoral depictions. With cavalry, each horse can carry a rider and that rider can use a weapon. With the Chinese chariot, the ration was four horses to one actual fighter (two fighters, but one for ranged and one for close combat, so effectively one fighter). Cavalry is four horses to four actual fighters (even though the versatility of the chariot crew might be higher). The downside was that being effectivy cavalry is a lifestyle choice. Riding in a chariot is a lot easier. This might also be the reason that the chariot was still in use, even after cavalry came into use.
Chariots are much more sensitive to bad going - horse cavalry can go places you could never get a chariot.
Although for the Chinese, as noted, the chariot in combat with the steppe horse archers had the problem of one archer for a three man crew. I would imagine that that chariot crew might end up being confronted by up to half a dozen horse archers who could overwhelm the lone archer in the chariot and them just stand off and kill the other crew.
goragrad, the Egyptian 2 man chariot was quite shockingly light, and the crew could dismount at the trot and easily lift it obstacles. This was not so of heavier 3 or 6 man chariots. Or SCh.
So not sure all chariots are equally affected by bad or rough. Choice of javelins or bows for use from a chariot could have had a massive impact on how they were used. Also until horse archers learned how to ride hard hands free while using a bow, chariots would have made a lot of sense. Having a driver and two "gunners" could have been quite effective.
I suspect chariots were expensive to make and maintain, and if essentially the same effect could be achieved with just horse and man, it is a cheaper and widely available option.
Declaring a War on Terror in response to 9/11 is like declaring a War on Torpedo Bombing in response to Pearl Harbour...