Large Language Models (LLMs) hold promise in addressing complex medical problems. However, while most prior studies focus on improving accuracy and reasoning abilities, a significant bottleneck in developing effective healthcare agents lies in the readability of LLM-generated responses, specifically, their ability to answer public health problems clearly and simply to people without medical backgrounds. In this work, we introduce RephQA, a benchmark for evaluating the readability of LLMs in public health question answering (QA). It contains 533 expert-reviewed QA pairs from 27 sources across 13 topics, and includes a proxy multiple-choice task to assess informativeness, along with two readability metrics: Flesch-Kincaid grade level and professional score. Evaluation of 25 LLMs reveals that most fail to meet readability standards, highlighting a gap between reasoning and effective communication. To address this, we explore four readability-enhancing strategies-standard prompting, chain-of-thought prompting, Group Relative Policy Optimization (GRPO), and a token-adapted variant. Token-adapted GRPO achieves the best results, advancing the development of more practical and user-friendly public health agents. These results represent a step toward building more practical agents for public health.