Entanglement swapping between photon pairs generated at physically separated nodes over telecommunication fiber infrastructure is an essential step towards the quantum internet, enabling applications such as quantum repeaters, blind quantum computing, distributed quantum computing, and distributed quantum sensing. However, successful networked entanglement swapping relies on generating indistinguishable pairs of photons and preserving them over deployed fibers. This has limited most previous demonstrations to laboratory settings or relied on sophisticated methods to maintain the necessary indistinguishability. Here, we demonstrate a scalable entanglement swapping experiment using naturally indistinguishable entanglement sources based on warm atomic vapor cells. Without sharing lasers or optical frequency references between nodes, nor the need for pulsing the sources, we achieve a swapping rate of nearly 500 pairs/s in a local configuration while maintaining the CHSH parameter above 2. Additionally, we demonstrate the scalability of our method by maintaining the quality of the entanglement swapping on 17.6 km of deployed fibers in NYC, relying on commercially available SPADs at the spoke nodes, SNSPDs at the hub and standard time-synchronization techniques. Our work paves the way for the practical deployment of large-scale hub-and-spoke quantum networks within cities and data centers.