Holographic displays are a promising technology for delivering immersive, true 3D visualization in virtual and augmented reality applications. However, generating high-fidelity phase-only holograms remains challenging, especially with the demand for efficient compression to handle the substantial data inherent in high-resolution holographic streaming. Existing techniques often struggle to balance the trade-off between optical display quality and compression efficiency, and jointly optimizing these aspects is still in its infancy. This work presents a learning-empowered multi-color hologram compression scheme that utilizes a pre-trained, camera-calibrated wave propagation model, especially for unfiltered holographic display configurations with compact form factors. In particular, the inter-color processing leverages the inherent redundancy across color channels, allowing for efficient compression. By incorporating the learned camera-calibrated wave propagation model into our training process, we can achieve superior optical display quality and compression rates. Experiments demonstrate that our method realizes a reduction in bits per pixel (bpp) of 44% to 74% over representative baselines at the same quality level. We envision the proposed compressive hologram synthesis scheme establishing a new benchmark for high-fidelity holographic reconstruction at lower bitrates, marking a significant advance towards the deployment of holography-empowered visual media systems.