A typical queen bank is very similar to a cell finisher colony. It’s a queen-right colony bubbling with bees, but where the queen is confined to the bottom box(es) with mostly sealed brood and plenty of space to keep laying. Above the excluder there is a source of honey, pollen, and mostly open brood draw the nurse bees up. The colony should be healthy and well feed. A frame with queens in cages can be inserted in the middle of the brood nest in the upper box and will get great attention by nurse bees.
But will all things like this, the question is who provides the resources and labor?
Who is going to create and maintain a cell builder colony? Colonies like this need close attention to keep hive resources properly distributed. Open brood should be rotated upstairs periodically, and feeding is usually performed.
If queens were to be purchased and then banked, who is responsible if any of the queens die?
Does the person managing the queen bank have time to accommodate those interesting in obtaining queens? Where would such a colony reside?
All this stuff can be done, but attention to detail and timing is critically important. It is worthy of discussion.
The next step of instead of just banking queens is to produce queen cells or queens. Queen breeders usually have cell starter colonies (to tend to grafted queen cells) and cell finisher colonies (to provide an environment for the queen cells to mature). Some use the same colony for both. A bee club can do these sort of things, but it takes dedicated and diligent volunteers, and probably a leader. Timing and implementation have to be done precisely or things won’t work.
Food for thought though .