Volumetric media promises next-generation content delivery applications, but its bandwidth demand remains a key bottleneck. Implicit and hybrid volumetric representations reduce model sizes, yet still require careful coding to reach 2D video-like bitrates. We present CATRF, a standard-codec-in-the-loop compression framework for plane-factorized radiance fields. During training, we quantize and pack 2D feature planes into codec-friendly canvases, run a standard codec roundtrip (JPEG/VP9/HEVC/AV1), then unpack and dequantize the decoded features before volume rendering. We use a straight-through estimator (STE) to insert the non-differentiable, standard codec pipeline into the training loop, allowing radiance-field features to adapt directly to the real, client-side codec distortions without introducing any learned codec parameters. On both static and dynamic benchmarks, CATRF consistently achieves a better rate-distortion trade-off over codec-agnostic and learned-codec-in-the-loop baselines, and also outperforms recent compressed 3DGS methods in both compression efficiency and decoding speed. These results highlight a practical path toward low-bitrate, compression-resilient volumetric representations for free-viewpoint video streaming.