What Drives Interactive Improvement from Feedback?

We study when natural-language feedback produces improvement beyond the gains obtainable from repeated attempts alone. In multi-turn language agent setting, higher final accuracy can reflect useful feedback, but it can also arise from resampling, format correction, or additional test-time computation. To separate these effects, we introduce a controlled student-teacher protocol across Omni-MATH, Codeforces, BBEH Linguini, and ARC-AGI1, evaluating thirteen open-weight models in both student and teacher roles. We compare external feedback, self-feedback, and unguided self-refinement, while varying interaction history, task difficulty, and teacher access to privileged task information. Across settings, we find that multi-turn improvement is often not evidence of feedback use: self-generated feedback adds little beyond unguided self-refinement, whereas the strongest external teachers produce substantially larger feedback-specific gains, suggesting that useful feedback must provide guidance beyond generic retry. Dense student-teacher interaction matrices further show that interactive gains are driven more by the student's ability to use feedback than by the teacher's identity, although teacher choice remains important for a fixed student. These results suggest that feedback-based agents should be evaluated against repeated-attempt baselines, and that ability to act on feedback, not merely feedback availability, is a central bottleneck for interactive improvement. We release our controlled student-teacher evaluation framework at https://j-lojek.github.io/feedback-generation-is-a-bottleneck/.