Modern LLMs inherit strong priors from web-scale pretraining, which can limit the headroom of post-training data-selection strategies. While Active Preference Learning (APL) seeks to optimize query efficiency in online Direct Preference Optimization (DPO), the inherent richness of on-policy candidate pools often renders simple Random sampling a surprisingly formidable baseline. We evaluate uncertainty-based APL against Random across harmlessness, helpfulness, and instruction-following settings, utilizing both reward models and LLM-as-a-judge proxies. We find that APL yields negligible improvements in proxy win-rates compared to Random. Crucially, we observe a dissociation where win-rate improves even as general capability -- measured by standard benchmarks -- degrades. APL fails to mitigate this capability collapse or reduce variance significantly better than random sampling. Our findings suggest that in the regime of strong pre-trained priors, the computational overhead of active selection is difficult to justify against the ``cheap diversity'' provided by simple random samples. Our code is available at https://github.com/BootsofLagrangian/random-vs-apl.