The infamous war chariots were used by middle eastern civilizations during antiquity, but then completely abandoned never to be seen again, replaced by regular cavalry. I get that horsemen where much cheaper and mobile than a chariot, but I think a dedicated scythe chariot unit would've been extremely effective at least during the early middle ages, no? Is there any evidence that indicates why the whole concept was ditched?
You've hit on the cost issue already, since 2 horses plus chariot is always going to be more expense and effort than 1 horse plus rider. But there are also other considerations at play. More can always be said about chariots and their intricacies, so if anyone else would like to address themselves to the topic, please don't let this post stop you!
For the meantime, OP, here are some previous posts on chariots for your perusal: