Annotating data remains a costly bottleneck for supervised NLP. Active learning (AL) reduces the number of human labels needed by selecting only the most informative instances, while instruction-tuned LLMs attack the same bottleneck from the other side, making labels cheap enough to annotate entire corpora. This raises two questions: can LLM labels replace human labels within the AL loop, and does AL remain necessary when entire corpora can be cheaply labeled? We investigate both by training supervised hate speech classifiers on a new dataset of 278K German political TikTok comments, comparing human and LLM annotation under matched conditions. LLM annotation at scale outperforms human-supervised classifiers at roughly one-tenth the cost, for both a closed-source (GPT-5.2) and an open-weight (Qwen3.5-122B-A10B) LLM, and the advantage is robust under soft-label evaluation. It hinges on the annotation interface: only a two-question decomposition mirroring the human annotation task unlocks it. AL provides no reliable advantage over random sampling in our prefiltered pool. Error structure depends on the LLM: only GPT-5.2 matches the human FP/FN balance, while other variants over-flag border-control and economic-competition discourse. Humans remain essential as evaluators; for training labels, the question shifts to which LLM, which interface, and what shape of pool.

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