A faster storage device should make serving faster. We find the opposite. High-Bandwidth Flash (HBF) stacks NAND behind a wide, package-local interface, promising flash-scale capacity with far lower read latency and higher bandwidth than an SSD. The obvious move is to keep an SSD-style Mooncake KV-offloading stack and swap in HBF underneath. We built that system and measured it: an extended TokenSim, four complete two-hour Qwen-Bailian production traces, five dense and mixture-of-experts models, and H100/B200 profiles. The upgrade backfires. Average end-to-end latency rises 2--5.5$\times$ and maximum SLO goodput falls 1.1--2.7$\times$ across H100 and B200, so the faster device yields a slower system. A cost-benefit model explains the paradox: a faster far tier pays off only when read I/O is the bottleneck, reads outweigh writes, and delivered bandwidth is sustainable. Transient KV violates all three at once. Buying flash through the package costs GPU near-tier capacity and bandwidth, while HBF's own read/write latency barely matters: scaling it 3.75$\times$ moves latency less than 1\%. Worse, the two-tier hierarchy keeps reuse in the near tier and hands HBF a relentless write-heavy stream. Writes outnumber reads on every trace, so a 3D-ICE model shows the stack hits its thermal limit well below peak bandwidth, and a TLC tier wears out sooner than the SSD pool it replaced. The device is fine; the drop-in deployment is not. HBF sucks as an SSD replacement for transient KV, but earns its place in LLM serving when used selectively with reuse-aware placement, write budgeting, and thermal coordination.

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