Storing as AP0 is not “better”. It’s just that it is the standard ACES approach, and what ACES is fundamentally about is defining standards, so everybody know where they are. But if you are in control of your own pipeline, and communicate clearly with all involved, there is nothing to stop you writing linear AWG to EXR files. Many facilities write ACEScg to EXRs internally, even though it is technically non-standard.
The conversion from AWG to AP0 is a simple 3x3 matrix, which is completely invertible. But half-float EXRs lose some granularity compared to the internal 32 or 64 bit processing in an app, so it’s possible you could see rounding errors in a round-trip to disk. But they should be very small. Are you seeing errors which actually produce visible artefacts?