No, 2 wheels in line are super stable with enough speed. Centrifugal forces due to rotation give the wheel it’s stability. It always wants to be upright. It’s like a gyroscope. The bigger the wheel the more stable it becomes. Speed is also important.
If you corner a chariot to fast it will topple over. Sure I can topple over on a motorcycle but that’s poor skill or bad decision making.
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.
Chariots are like trikes and trikes have a different issue with stability. Having two wheels like a hoverboard/segue requires technology to balance for you. It’s not so much new science but packaging gyroscopes and drive power had been difficult for a long time. A two wheel unicycle sounds miserable. The gyroscopic effect helps balance the bike in the same direction the bike wheel rotates and you have two in a row so it’s harder to just end up on your back or face. If you don’t have something keeping you from doing that moving would require lots of skill.
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