I suspect the flat contact patch would alter the efficacy of beads at balancing a wheel. That would force movement that may counteract the balancing properties, and could even result in unwanted oscillations.
As to how the balancers work:
The beads (or balancing material) is driven to the farthest point due to the acceleration forces. This movement alters the center of gravity. A body in space will freely rotate about its center of gravity, and not whatever geometric center may exist.
Think about the spin in a hammer throw.
Even though the system appears unbalanced, it actually is balanced; however, it isn't rotating about the human, but an imaginary axis in between the human and the weight. If you were to put a ball on a string and attach it to the thrower's head, it would eventually sit directly behind the thrower's head, bringing the actual axis of rotation closer to the axis of the human body.
Since the wheels are isolated by the tire and the vehicle suspension, they have a tendency to rotate around their center of gravity. If that isn't concentric with the axle tube, the axle tube is forced to oscillate as a result. But the axle tube provides a restorative force that forces the beads to realign at the farthest away point, ultimately bringing the axis of rotation inline with the axle tube.
This process breaks down when there is insufficient compliance in the axle tube. Fir example, if you took the car with beads or Centramatics and put it on jackstands on the axle tubes and ran it up to freeway speeds, the restorative force from the axle tubes would be altered, the material would fly to one side, and the wheel would violently shake until the whole car falls off the stands.
Here is a brief overview of how Centramatics work:
https://www.centramatic.com/faq.rhtml