Accurate detection of third-party libraries (TPLs) is fundamental to Android security, supporting vulnerability tracking, malware detection, and supply chain auditing. Despite many proposed tools, their real-world effectiveness remains unclear. We present the first large-scale empirical study of ten state-of-the-art TPL detection techniques across over 6,000 apps, enabled by a new ground truth dataset with precise version-level annotations for both remote and local dependencies. Our evaluation exposes tool fragility to R8-era transformations, weak version discrimination, inaccurate correspondence of candidate libraries, difficulty in generalizing similarity thresholds, and prohibitive runtime/memory overheads at scale. Beyond tool assessment, we further analyze how TPLs shape downstream tasks, including vulnerability analysis, malware detection, secret leakage assessment, and LLM-based evaluation. From this perspective, our study provides concrete insights into how TPL characteristics affect these tasks and informs future improvements in security analysis.