I have to disagree. I find that Chariots in open terrain can munch Warriors, hold their own against Archers and fare very well against Axemen. Swordsmen, of course, eat them alive. But in the early game I find them indispensible in holding the Barbs at bay. Archers defend well, but are poor attack dogs against Axes and easy pickings for Swords.
The problem though is that in order to get chariots, you have the same problem as with relying on axemen/spearmen rather than archers for defense against barbs. You need ready access to a resource and then roads to hook it up. That takes time, in marathon speed a LOT of time. (but everything being proportionally faster the same problem should exist in faster game speeds as well).
And in Emperor level, the AIs are building cities left and right you cannot stop to build a worker, then build mine then roads. The horse or bronze may not be within your borders even (though hopefully within close proximity so that you can build a city near it). But if you are spending time building a worker then you've just delayed founding that new city that you may need to found to access the horse/bronze not to mention the AI has now perhaps a better chance to grab that horse or bronze instead of you since you've delayed yourself in building another settler in favor of a worker.
The beauty of archery is that it requires NO resources and no infrastructure and is much less research intensive than either AH or BW. Many leader start with hunting but even if you don't have hunting, hunting->archery path is still pretty fast.
In lower game levels probably it is not so necessary to race with the AIs to found cities so sparing production for a worker and hooking up horse or bronze is doable. But in Emperor or even Monarch level, the time simply isn't there.
For playing at Monarch or certainly Emperor where you are in a race to grab lands quickly, archery is your only real option. You cannot bypass it in favor of chariots or axeman/spearman.
And furthermore, you will NOT be facing a whole bunch of warriors or even archers. Most barbs are archers and quite a few axeman. AIs quickly hook up their bronze or iron and begin producing axeman, spearman, swordsmen very quickly. And since chariots are fodder against swordsmen and are only okay against axeman, I always emphasize bronze or if bronze is not available, then iron. I have fought many a war with chariots against metal-based armies of axeman and swordsmen and it is a lost cause! (and I only did it because there was no bronze/iron access only horse)
For these reasons, I race to try to get bronze or iron and build up my axeman army ASAP. Even if I have horses, I don't build hardly any chariots (although due to their faster speed they make good pillagers). But that is more a luxury and I will certainly build up metal mines and axeman divisions first.
For higher levels of play where racing against the AIs for cities is a must, archery is a must. There is no time for building the infrastruture for chariots or axeman (nevermind the time to build axeman or chariots themselves). You are racing against the AI for cities. Furthermore unless you are lucky and have ready access to horse or bronze, you will not be able to build up that infrastruture which allows you to build chariots to fight barbarians when they appear as early as 2500BC!
