How can we design a market of human-generated content for use in training AI models that both enables technological progress and preserves individual incentives for high-quality content creation? Existing approaches take polar positions: a "free-for-all" model based on fair use and a "strong intellectual property rights" model. We show that both fail: Free-for-all does not compensate creators, and -- by modeling as a static Stackelberg game -- strong intellectual property rights also underpower creative incentives. We find this especially true for more innovative creators, a phenomenon we term the "originality penalty." Extending this insight to a dynamic model, we find another market failure undermining AI model performance, even for an initially good model: Such a model induces greater reliance by humans on AI-assisted creation, resulting in homogenized content feeding back into training, which degrades the model performance -- a "curse of precision." We further propose a market design with a data intermediary internalizing cross-creator externalities and subsidizing innovative contributions, thereby restoring efficiency.