Recent progress in reasoning-oriented Large Language Models (LLMs) has been driven by introducing Chain-of-Thought (CoT) traces, where models generate intermediate reasoning traces before producing an answer. These traces, as in DeepSeek R1, are not only used to guide inference but also serve as supervision signals for distillation into smaller models. A common but often implicit assumption is that CoT traces should be semantically meaningful and interpretable to the end user. While recent research questions the need for semantic nature of these traces, in this paper, we ask: ``\textit{Must CoT reasoning traces be interpretable to enhance LLM task performance?}" We investigate this question in the Open Book Question-Answering domain by supervised fine-tuning LLaMA and Qwen models on four types of reasoning traces: (1) DeepSeek R1 traces, (2) LLM-generated summaries of R1 traces, (3) LLM-generated post-hoc explanations of R1 traces, and (4) algorithmically generated verifiably correct traces. To quantify the trade-off between interpretability and performance, we further conduct a human-subject study with 100 participants rating the interpretability of each trace type. Our results reveal a striking mismatch: while fine-tuning on R1 traces yields the strongest performance, participants judged these traces to be the least interpretable. These findings suggest that it is useful to decouple intermediate tokens from end user interpretability.