Neural audio codecs optimized for mel-spectrogram reconstruction often fail to preserve intelligibility. While semantic encoder distillation improves encoded representations, it does not guarantee content preservation in reconstructed speech. In this work, we demonstrate that self-supervised representation reconstruction (SSRR) loss fundamentally improves codec training and performance. First, SSRR significantly accelerates convergence, enabling competitive results using only a single GPU. Second, it enhances intelligibility by reconstructing distilled self-supervised representations from codec outputs. Third, SSRR enables high intelligibility without additional lookahead in streaming Transformer-based codecs, allowing a zero-lookahead architecture for real-time deployment. As a result, our JHCodec achieves state-of-the-art performance while maintaining minimal latency and reduced training cost. We open-source the full implementation, training pipeline, and demo on Github https://github.com/jhcodec843/jhcodec.