When working with generative artificial intelligence (AI), users may see productivity gains, but the AI-generated content may not match their preferences exactly. To study this effect, we introduce a Bayesian framework in which heterogeneous users choose how much information to share with the AI, facing a trade-off between output fidelity and communication cost. We show that the interplay between these individual-level decisions and AI training may lead to societal challenges. Outputs may become more homogenized, especially when the AI is trained on AI-generated content, potentially triggering a homogenization death spiral. And any AI bias may propagate to become societal bias. A solution to the homogenization and bias issues is to reduce human-AI interaction frictions and enable users to flexibly share information, leading to personalized outputs without sacrificing productivity.