Presumably because chariots are currently still statistically identical to cavalry. Moreover, most chariots are champions trainable at the fortress (brit, maur, sele); only the Persian chariots are not; they count as citizen cavalry trainable at the stable. Personally I'd favour replacing the Persian b/a/e chariot archers with ordinary horse archers and introducing a champion scythed chariot (cf. Seleucids).
And yeah, I agree the workshop could be a more appropiate structure for chariots than the stable. In fact, I've implemented that in my 0abc mod months ago.