Ants actually have a completely decentralized system of organizing labor. Each worker forages and scouts autonomously until they find something interesting for the collective, after which they chemically mark the newly discovered ressource. Other ants then follow this trail, which automatically makes them form an organized group that distributes labor evenly to transport the ressource back to the nest. Likewise, all gathered food is shared collectively.

The queen does zero organizational work and has no command over her workers, she just lays eggs to produce more workers. She's as much a part of the collective as any worker ant, only serving a different purpose due to her reproductive ability, and in fact larger colonies tend to have multiple queens in most species. Calling her a queen is anthropomorphizing the relation she has to the rest of the colony, which aren't her subjects, but her children or, in a multi-queen colony, her nieces.