Face recognition in unconstrained environments such as surveillance, video, and web imagery must contend with extreme variation in pose, blur, illumination, and occlusion, where conventional visual quality metrics fail to predict whether inputs are truly recognizable to the deployed encoder. Existing FIQA methods typically rely on visual heuristics, curated annotations, or computationally intensive generative pipelines, leaving their predictions detached from the encoder's decision geometry. We introduce TransFIRA (Transfer Learning for Face Image Recognizability Assessment), a lightweight and annotation-free framework that grounds recognizability directly in embedding space. TransFIRA delivers three advances: (i) a definition of recognizability via class-center similarity (CCS) and class-center angular separation (CCAS), yielding the first natural, decision-boundary-aligned criterion for filtering and weighting; (ii) a recognizability-informed aggregation strategy that achieves state-of-the-art verification accuracy on BRIAR and IJB-C while nearly doubling correlation with true recognizability, all without external labels, heuristics, or backbone-specific training; and (iii) new extensions beyond faces, including encoder-grounded explainability that reveals how degradations and subject-specific factors affect recognizability, and the first method for body recognizability assessment. Experiments confirm state-of-the-art results on faces, strong performance on body recognition, and robustness under cross-dataset shifts and out-of-distribution evaluation. Together, these contributions establish TransFIRA as a unified, geometry-driven framework for recognizability assessment that is encoder-specific, accurate, interpretable, and extensible across modalities, significantly advancing FIQA in accuracy, explainability, and scope.