Propose an allocation, and commit it only when asked.

THE POINT: the allocator proposes and an admin commits. The response is a table an operator reads and adjusts, and a case nothing could be proposed for comes back in unassigned WITH A REASON rather than quietly vanishing from the list.

Committing writes assignments rows, which are a PRIORITY and not a permission: an assigned case sorts to the top of its assignee's queue and every other physician still sees it exactly where it was. Nothing about who MAY draw a case changes here.