Widely adopted evaluation metrics for sparse-view CT reconstruction, such as Structural Similarity Index Measure and Peak Signal-to-Noise Ratio, prioritize pixel-wise fidelity but often fail to capture the completeness of critical anatomical structures, particularly small or thin regions that are easily missed. To address this limitation, we propose a suite of novel anatomy-aware evaluation metrics designed to assess structural completeness across anatomical structures, including large organs, small organs, intestines, and vessels. Building on these metrics, we introduce CARE, a Completeness-Aware Reconstruction Enhancement framework that incorporates structural penalties during training to encourage anatomical preservation of significant structures. CARE is model-agnostic and can be seamlessly integrated into analytical, implicit, and generative methods. When applied to these methods, CARE substantially improves structural completeness in CT reconstructions, achieving up to 32% improvement for large organs, 22% for small organs, 40% for intestines, and 36% for vessels.