Don’t forget that chariots don’t just have two wheels: they also have one or more horses attached to the front, providing balance.
Once you get a little speed, physical forces will tend to keep a wheel from falling left or right…but if you’re on a unicycle, there’s nothing preventing you from falling forward or backward. On a bicycle, the two wheels give you forward-backward stability and the gyroscopic effects give you left/right stability.
On a chariot, the two wheels give you left/right stability (conveniently, even when you’re not moving), and you get your front/back stability from the chariot’s attachment to the horse(s). Without those horses, you’ll have to balance yourself. Devices like hoverboards or Segways with that wheel configuration have gyroscopes in the appropriate orientation to keep you from falling forward/back.
You could also solve the problem by having two big side-by-side wheels and a smaller wheel to the forward or back…which we call a tricycle. Or two big side-by-side wheels for propulsion and two small wheels in the front for stability like a wheelchair.
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