Text normalization methods such as stemming and lemmatization are fundamental components of NLP pipelines. As new normalization tools are developed for diverse languages, evaluation methodologies remain fragmented, relying on Compression Ratio, downstream accuracy, or sequence-to-sequence prediction scores in isolation, failing to distinguish between beneficial vocabulary reduction and harmful semantic distortion. Moreover, text normalization underpins intelligent systems in high-stakes domains, including clinical decision support and legal document analysis, and principled evaluation methodology is essential. This paper proposes NormEval, a unified, multilingual evaluation framework comprising five complementary metrics: Compression Ratio (CR), Model Performance Delta (MPD), Information Retention Score (IRS), Algorithm Effectiveness Score (AES), and Average Normalized Levenshtein Distance (ANLD). These metrics assess normalization quality across three dimensions: macro-level efficiency, downstream utility, and micro-level morphological fidelity. The framework operationalizes a Safety Gate hypothesis: ANLD functions as an intrinsic structural hygiene check, utilizing character-level divergence ($Δ$) to reveal aggressive mutations that macro-level embeddings and downstream tasks mask. Comprehensive ablation experiments on both Bangla and English datasets show that all the components are indispensable, and that the removal of any individual metric leads to a decrease in at least one evaluation aspect, which ultimately results in misleading algorithm rankings.