The rapid shift from stateless large language models (LLMs) to autonomous, goal-driven agents raises a central question: When is agentic AI truly necessary? While agents enable multi-step reasoning, persistent memory, and tool orchestration, deploying them indiscriminately leads to higher cost, complexity, and risk. We present STRIDE (Systematic Task Reasoning Intelligence Deployment Evaluator), a framework that provides principled recommendations for selecting between three modalities: (i) direct LLM calls, (ii) guided AI assistants, and (iii) fully autonomous agentic AI. STRIDE integrates structured task decomposition, dynamism attribution, and self-reflection requirement analysis to produce an Agentic Suitability Score, ensuring that full agentic autonomy is reserved for tasks with inherent dynamism or evolving context. Evaluated across 30 real-world tasks spanning SRE, compliance, and enterprise automation, STRIDE achieved 92% accuracy in modality selection, reduced unnecessary agent deployments by 45%, and cut resource costs by 37%. Expert validation over six months in SRE and compliance domains confirmed its practical utility, with domain specialists agreeing that STRIDE effectively distinguishes between tasks requiring simple LLM calls, guided assistants, or full agentic autonomy. This work reframes agent adoption as a necessity-driven design decision, ensuring autonomy is applied only when its benefits justify the costs.