Uh?
What do you mean by static balance here? I'd interpret that as balncing a non rotating wheel, say by hanging it from the hub centre and putting weights on it, or putting it on a low friction axle. That self-evidently is not what is happening with loose beads inside a tyre.
As described the tyre is unbalanced when static and only becomes balanced when rotation redistributes the beads.
Pretty much the opposite of static balancing, IOW
I think you're getting confused by the terminology.
Static balance - aka bubble balancing - can be done without spinning the tire. The result is placing weights evenly distributed side to side.
Dynamic balancing requires spinning the tire and the result is usually placing different amount of weights side to side and in different locations circumferentially.
So, yes, the balance beads (or liquid) only work when the tire is rolling - and I can see why they might have difficulty dealing with a situation where the required balancing weight is off center (aka as dynamic balancing) - and full disclosure: I am not a fan of balancing beads and compounds - but I am wondering what speed is required to overcome gravity enough to be effective.