Yeah, it seems this free-rotating design would keep one side down if the center of gravity is not exatly on the intersection of all rotation axes. This might be worse than a common single-axis cooking.
I watched the short gif/video and I had the same thought. If you don't pierce the object/meat in a manner that its centre of gravity is on the very centre of this contraption, it would skew the spin and it affect its randomness in the movement.
But totally a fun project and cool topic to discuss on any BBQ
But totally a fun project and cool topic to discuss on any BBQ