Large language models (LLMs) hold promise for advancing patient–provider communication, yet a persistent gap remains between benchmark-driven model development and the realities of clinical practice. This work presents a systematic, clinically grounded review of text-based medical datasets for LLM training and evaluation. We propose a scenario-based taxonomy derived from established clinical frameworks to map major knowledge-based and conversation-based corpora against core communication scenarios. We further synthesize core communication skills from gold-standard clinical assessment instruments and meta-analyze state-of-the-art medical LLM performance, highlighting how dataset properties, fine-tuning strategies, and evaluation metrics shape both knowledge acquisition and communicative competence. To empirically validate these findings, we conducted controlled fine-tuning experiments across representative LLMs, demonstrating that data composition and scenario alignment critically affect model performance. Our findings highlight the urgent need for scenario-rich datasets and standardized, human-centered evaluation protocol to advance clinically relevant medical LLMs.