Context: AI coding agents route every task to a single frontier large language model (LLM), paying premium inference cost even when many tasks are routine. Objectives: We propose Triage, a framework that uses code health metrics -- indicators of software maintainability -- as a routing signal to assign each task to the cheapest model tier whose output passes the same verification gate as the expensive model. Methods: Triage defines three capability tiers (light, standard, heavy -- mirroring, e.g., Haiku, Sonnet, Opus) and routes tasks based on pre-computed code health sub-factors and task metadata. We design an evaluation comparing three routing policies on SWE-bench Lite (300 tasks across three model tiers): heuristic thresholds, a trained ML classifier, and a perfect-hindsight oracle. Results: We analytically derived two falsifiable conditions under which the tier-dependent asymmetry (medium LLMs benefit from clean code while frontier models do not) yields cost-effective routing: the light-tier pass rate on healthy code must exceed the inter-tier cost ratio, and code health must discriminate the required model tier with at least a small effect size ($\hat{p} \geq 0.56$). Conclusion: Triage transforms a diagnostic code quality metric into an actionable model-selection signal. We present a rigorous evaluation protocol to test the cost--quality trade-off and identify which code health sub-factors drive routing decisions.