Should This Task Get Tree-of-Thought?

A teammate proposes adding tree-of-thought search to your product's "generate a personalized 4-week workout plan given user constraints" feature, arguing "there are lots of possible plans, so search should help us find a better one." The feature currently uses a single CoT prompt, runs about 50,000 times/day, and a recent eval shows the single-prompt version satisfies all stated user constraints (injury limits, equipment, days available) 88% of the time, with the 12% failures roughly evenly spread across "missed one minor constraint" and "plan is technically valid but low quality/repetitive."

1. Evaluate the teammate's argument for tree-of-thought specifically — is "many possible outputs exist" sufficient justification?
2. What does the failure breakdown (missed-constraint vs. low-quality) tell you about which technique, if any, is actually indicated?
3. Propose a concrete next step, with a rough cost estimate at the current volume, and explain why you'd measure before committing.