As LLMs are globally deployed, aligning their cultural value orientations is critical for safety and user engagement. However, existing benchmarks face the Construct-Composition-Context ($C^3$) challenge: relying on discriminative, multiple-choice formats that probe value knowledge rather than true orientations, overlook subcultural heterogeneity, and mismatch with real-world open-ended generation. We introduce DOVE, a distributional evaluation framework that directly compares human-written text distributions with LLM-generated outputs. DOVE utilizes a rate-distortion variational optimization objective to construct a compact value codebook from 10K documents, mapping text into a structured value space to filter semantic noise. Alignment is measured using unbalanced optimal transport, capturing intra-cultural distributional structures and subgroup diversity. Experiments across 12 LLMs show that DOVE achieves superior predictive validity, attaining a 31.56% correlation with downstream tasks, while maintaining high reliability with as few as 500 samples per culture.