LLM-enabled applications are rapidly reshaping the software ecosystem by using large language models as core reasoning components for complex task execution. This paradigm shift, however, introduces fundamentally new reliability challenges and significantly expands the security attack surface, due to the non-deterministic, learning-driven, and difficult-to-verify nature of LLM behavior. In light of these emerging and unavoidable safety challenges, we argue that such risks should be treated as expected operational conditions rather than exceptional events, necessitating a dedicated incident-response perspective. Consequently, the primary barrier to trustworthy deployment is not further improving model capability but establishing system-level threat monitoring mechanisms that can detect and contextualize security-relevant anomalies after deployment -- an aspect largely underexplored beyond testing or guardrail-based defenses. Accordingly, this position paper advocates systematic and comprehensive monitoring of security threats in LLM-enabled applications as a prerequisite for reliable operation and a foundation for dedicated incident-response frameworks.