I don’t think the writer should do this (it’s up to the operators upstream to decide if a nodata value makes sense). NaN isn’t problematic most of the time , but if you’re not paying attention and you convert a SNAP output to an integer format, implementations like GDAL will convert the NaN nodata value to 0, potentially causing problems later on. It’s also wrong if the source band already has a nodata value set.
In addition, this is only done for Float32 bands. Float64 bands don’t get a nodata value.
Issue introduced during the fix for SNAP-3721.