Educational diagrams -- labeled illustrations of biological processes, chemical structures, physical systems, and mathematical concepts -- are essential cognitive tools in K-12 instruction. Yet no existing method can generate them both accurately and engagingly. Open-source diffusion models produce visually rich images but catastrophically garble text labels. Code-based generation via LLMs guarantees label correctness but yields visually flat outputs. Closed-source APIs partially bridge this gap but remain unreliable and prohibitively expensive at educational scale. We quantify this accuracy-aesthetics dilemma across all three paradigms on 400 K-12 diagram prompts, measuring both label fidelity and visual quality through complementary automated and human evaluation protocols. To resolve it, we propose CAGE (Code-Anchored Generative Enhancement): an LLM synthesizes executable code producing a structurally correct diagram, then a diffusion model conditioned on the programmatic output via ControlNet refines it into a visually polished graphic while preserving label fidelity. We also introduce EduDiagram-2K, a collection of 2,000 paired programmatic-stylized diagrams enabling this pipeline, and present proof-of-concept results and a research agenda for the multimedia community.