We investigate learned KV cache compression through Speculative Importance Prediction (SIP), a 1.7M parameter non-query-aware scorer that predicts token importance from KV representations alone. Despite architectural sophistication (multi-horizon lookahead, cross-attention), SIP does not outperform simple baselines, including random selection, across 5 seeds, 4 retention levels, and 3 tasks. Key findings: (1) position-based heuristics (keep first 4 + last N tokens) match or exceed learned approaches; (2) prefill attention provides equivalent signal to complex learned scorers; (3) marginal information in KV representations beyond position and prefill attention appears limited for importance prediction. We hypothesize that circular dependence between future queries and generation trajectories contributes to this difficulty.