KV cache compression is critical for long-context LLM inference, yet existing training-free methods fall into a dilemma: attention-based eviction clusters retained tokens around semantically “hot” regions, creating context holes that degrade long-range reasoning, while diversity-based selection retains directionally broad but semantically irrelevant tokens. We identify the root cause: at prefill time, future decoding queries are unknown, making query-conditioned signals unreliable as a sole selection criterion. The retained KV set must instead provide broad directional coverage of the context—so that arbitrary future queries can find supporting keys—while filtering out tokens that expand the coverage span without contributing to generation. We propose AnchorKV, which realizes this principle through block-wise partitioning with uniform per-block budgets and anchor-driven cosine dissimilarity scoring for linear-time diversity estimation. A compression-rate adaptive hybrid score dynamically reweights diversity and importance. Experiments on LongBench across three model families show AnchorKV consistently outperforms existing training-free methods, with the largest margins at low retention ratios. A query-subsampled variant reduces prefill latency by up to 2.7× with minimal accuracy loss. We provide theoretical guarantees on approximation error and variance reduction.