Large language models (LLMs) and cross-encoder rerankers have gained attention for improving recommender systems, particularly in cold-start scenarios where user interaction history is limited. However, practical deployment reveals significant performance gaps between LLM-based approaches and simple baselines. This paper presents a systematic diagnostic study of cross-encoder rerankers in cold-start movie recommendation using the Serendipity-2018 dataset. Through controlled experiments with 500 users across multiple random seeds, we identify three critical failure modes: (1) low retrieval coverage in candidate generation (recall@200 = 0.109 vs. 0.609 for baselines), (2) severe exposure bias with rerankers concentrating recommendations on 3 unique items versus 497 for random baseline, and (3) minimal score discrimination between relevant and irrelevant items (mean difference = 0.098, Cohen's d = 0.13). We demonstrate that popularity-based ranking substantially outperforms LLM reranking (HR@10: 0.268 vs. 0.008, p < 0.001), with the performance gap primarily attributable to retrieval stage limitations rather than reranker capacity. Based on these findings, we provide actionable recommendations including hybrid retrieval strategies, candidate pool size optimization, and score calibration techniques. All code, configurations, and experimental results are made available for reproducibility.