Clearly the evidence disproves the necessity of those. They may help though, but sifting the BBs out is an extra step from sifting the excess powder unless you have the perfect mesh size.
I think any residual moisture is the biggest limiting problem.
Even if the plastic is less than ideal, just wait a few more minutes and it seems to work out. I do think the dillon tumbler is a plus because it is a thick softer plastic and has a rubber gasket. But that's only relevant to keeping down noise and dust.

The nicest setup I could picture would be a dedicated tumbler with something fitted to it like a deep fryer basket made from plastic. That way you could just lift it up and lock it a bit above the bowl and vibrate for a minute to rattle all the excess dust off. Then simply pour out the basket onto your baking mesh.