KV cache offloading enables long-context LLM inference by storing caches in CPU DRAM, but PCIe bandwidth limitations create severe bottlenecks. In this paper, we develops an analytical framework that derives $\kappa_{\text{crit}}$, the critical cached-to-prefill token ratio where execution becomes memory-bound and show typical workloads exceed this threshold by orders of magnitude. Empirical characterization reveals 99\% of latency spent on transfers and serving offloaded requests results in GPU's consuming only 28\% of their rated TDP, motivating our proposed optimizations for hardware interconnects, model architectures, and scheduling algorithms.