KV cache eviction must decide which entries carry information that the rest of the cache can no longer supply. A natural way to estimate this is a learnable gate: give each cached entry a gate on its attention weight and train the gate on the model's own objective. The gate belongs inside the normalizing softmax, where suppressing one entry hands its mass to the others rather than discarding it. That same normalizer absorbs any per-query constant, so a constant gate cancels and reproduces the frozen model exactly. Trained on the language-modeling loss the gate stays near a constant score while its loss falls throughout: optimization succeeds, but a frozen backbone was fit for dense attention, so its loss prefers the no-op, and a near-constant score ranks nothing. The no-op is not a floor the gate improves from but what its objective asks for. A second obstacle survives once the gate moves, since the same gradient charges the gate for errors the frozen model already makes, which no reweighting of positions separates out. Much of the machinery in learnable eviction, from sparsity penalties to relaxations of the discrete decision, works around the first obstacle rather than removing it; both are removed by putting dense attention beyond the gate's reach and making the dense model's predictions its target. Under these two conditions capacity is never the missing ingredient: neither a larger scorer, nor explicit access to the past, nor a trainable backbone helps. The same holds for what eviction unavoidably discards, which is recovered by parameter-free centroids read inside the same softmax far better than by any memory read outside it, since the mass they must return is a share of that normalizer and available nowhere else. At 75\% KV cache compression, this gate reaches 90.14 on RULER at 8K and 46.03 on LongBench with Qwen3-8B, 3.72 and 1.36 points below full-cache inference.

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