Keeping runtime alive is critical for mitigating cold start issues in Function-as-a-Service (FaaS) platforms. State-of-the-Art (SOTA) keep-alive policies often draw an analogy to data caching, adapting classic replacement algorithms to manage runtime pools. Our analysis reveals that this analogy is fundamentally flawed: 1) they violate their own eviction priorities due to conflicts with running containers, and 2) they ignore the exorbitant memory-time resource cost of runtime replacement. To address these challenges, we present FaaShadow, a lightweight keep-alive policy that recasts the problem from simple caching to cost-aware resource allocation. FaaShadow introduces the concept of a shadow pool, a per-function data structure that enables online estimation of the marginal utility of memory adjustments. By quantifying both the potential performance gain from allocating new containers and the performance loss from removing existing ones, FaaShadow makes data-driven reallocation decisions that maximize the global warm start rate. Experimental results show that FaaShadow achieves a 95% warm start rate using only 60% of the memory required by the best-in-class baseline. When paired with our dynamic scaling mechanism, FaaShadow reduces average memory consumption by a staggering 81.71% compared to the SOTA predictive scaler, while upholding performance targets.