LLM agent memory modules universally adopt a single global retrieval depth k across all deployment scenarios; this global constraint produces an irreducible Oracle performance gap. We carry out a systematic evaluation on 19 heterogeneous deployment cells covering three LLM backbones, three multi-agent coordinators, three tasks, and two representative memory architectures (A-Mem and G-Memory). We confirm that the per-cell optimal k varies dramatically across cells, that low-capacity LLMs exhibit catastrophic accuracy collapse at larger k , and that no cross-cell feature or lookup-table shortcut reliably predicts the per-cell optimum. A theoretical analysis further shows that in the small-budget paired-binary-reward regime, every training-free bandit method we evaluate reduces to uniform-mean argmax. Motivated by this collapse, we propose per-cell warmup calibration: paired probe queries iteratively estimate the mean reward of each candidate k, the procedure commits to the empirical argmax, and a closed-form (2 σ) criterion provides earlystop. The recipe is training-free, requires no architectural modification, and introduces no hyperparameter beyond the probe budget. On all 19 deployment cells it attains 100% of the per-cell Oracle, with an average absolute improvement of +3.33 percentage points and a peak gain of +12.00 percentage points.