While prompt caching and batching are indeed effective strategies for reducing LLM inference costs, I maintain that model distillation and quantization provide superior cost-per-quality tradeoffs in the long run. Distillation transforms the knowledge of a large model into a smaller, specialized one, enabling significant reductions in latency and computational resource usage without a proportional loss in quality. For instance, NVIDIA's guide on inference optimization highlights that a well-distilled student model can achieve near parity with its teacher while being significantly cheaper to deploy (NVIDIA Developer, 2023). 

Quantization complements this by reducing the precision of the model's weights, allowing for even faster inference speeds and lower memory usage. According to MarkTechPost, these techniques, combined with others like pruning, can lead to a holistic optimization strategy that balances quality and efficiency (MarkTechPost, 2024).

While I acknowledge the merits of prompt caching and routing strategies, their effectiveness may diminish with more complex queries where the smaller models could falter. On the other hand, model distillation and quantization consistently maintain high performance across a broader range of tasks, making them a robust long-term solution for cost reduction in LLM deployments.