I did exactly like I posted above with 01m data. Those two examples, one assigning CRS using gdal_edit.py, the other using gmt grdedit. I’ve got exactly the same results, so not posting anything here. gdal_edit.py assigned CRS correctly, gmt grdedit quietly failed
gmt grdimage @earth_gebco_01m_p -n+a -Aworld.tiff -J4326 produces error messages like below which seems like gdal errors (gdal seems to be called by grdimage internally to produce the .tiff?). However, the resulting images are totally fine.
ERROR 10: Pointer 'hTransform' is NULL in 'OCTTransform'.
ERROR 10: Pointer 'hTransform' is NULL in 'OCTTransform'.
ERROR 10: Pointer 'hTransform' is NULL in 'OCTTransform'.
More than 1000 errors or warnings have been reported. No more will be reported from now.