The Mixture-of-Experts (MoE) architecture is crucial for scaling large language models, but its scalability is severely limited by inter-GPU communication bottlenecks in multi-GPU systems. Although overlapping communication with computation is a widely recognized optimization, its effective deployment still remains challenging, both in terms of performance and programmability. In this work, we identify the root cause as a fundamental abstraction mismatch between MoE's dynamic, irregular token-to-expert mapping and the static, address-centric communication model of modern GPUs, which necessitates a complex software mediation phase to resolve addresses before data transfers, limiting performance and software flexibility. To resolve this, we propose MoE-Hub, a hardware-software co-design that introduces a destination-agnostic communication paradigm. MoE-Hub decouples data transmission from address management, allowing producers to send data immediately after routing using only a logical destination, while address allocation and data-flow orchestration are handled transparently by lightweight hardware in the GPU hub. By hardware-accelerating the entire communication control plane, MoE-Hub enables seamless and transparent overlap. Our evaluation shows that MoE-Hub achieves 1.40x-3.08x per-layer and 1.21x-1.98x end-to-end speedup over state-of-the-art systems.