While Large Language Models (LLMs) have significantly advanced the fluency of Emotional Support Conversation (ESC) systems, current research predominantly focuses on engineering increasingly complex architectures—from intricate reasoning chains to multi-agent collaborations. While these advancements (e.g., CoT) offer semantic traces of reasoning, they remain mechanistically opaque, obscuring the fundamental causal mechanisms between dialogue features and effective empathic strategies, leading to poor interpretability and susceptibility to distribution shifts in offline learning. To address these limitations, we propose a novel framework Causal-ESC. Departing from conventional paradigms that directly utilize raw dialogue history as input, our approach introduces Doubly Robust (DR) learning to explicitly model the causal effect of utterance features on strategy selection, effectively mitigating the biases and counterfactual unobservability inherent in offline datasets. We further integrate an LLM-based stylized rewriting mechanism to translate these rigorously learned causal strategies into natural, context-consistent responses. Comprehensive experiments, supported by statistical verification (e.g., Outcome R²) and human-like evaluation, demonstrate that our framework not only significantly outperforms state-of-the-art baselines in empathy and helpfulness but also provides a theoretically grounded, interpretable solution to the mechanistic interpretability dilemma in affective computing.