I would imagine the beads would congregate in the location of highest eccentricity and make any imbalance worse. This is clearly wrong.
Yup, it's wrong. This is one of those things that is not intuitive.
Pardon my clumsy drawings. This is a wheel. It is statically balanced. It will rotate around its central axis, since its weight is evenly distributed around the wheel.
Now, if there is a heavy spot (the red square),
the wheel will want to rotate around the center of gravity, which has moved toward that heavy spot:
The balancing beads will want to go toward the farthest point away from the rotational axis, which is the eccentricity, as you state, and will counter the heavy spot's pull:
Once balance is achieved, the beads will spread out some to maintain the balance. If all the beads are too much and go to one spot and overbalance it, they will move apart toward the eccentricity that has developed opposite them until they have balanced the wheel.
There IS a difference between static and dynamic imbalance, a big difference:
The beads can handle the static imbalance, but how do you get them to ride up in the sidewall to correct dynamic imbalance? They're not going to settle for that.
That dynamically-imbalanced wheel could easily be statically balanced as it is in the picture. No vertical hopping, but certainly shimmying. Imagine, now, a wheel with a heavy spot like this:
It is both statically and dynamically imbalanced. Extra weight in one place, offset from the rotational plane of the wheel. The weight pulls itself over to the plane of rotation. If a mechanic statically balances it, he might put the balance weight diametrically opposite the heavy spot but on the other side of the wheel, and now it's statically balanced, but its shimmy will be WAY worse, like the dynamically imbalanced wheel in the diagram above it.
The only way to dynamically balance a wheel is to rotate it to make it shimmy to find its heavy spots. No static balancer can do that.