QGIS Custom Projection in WKT not saving .prj file

Question

I've created a Custom Projection System in QGIS using the WKT format (see code below). The custom projection using a local grid system and transforms it GDA94 / MGA zone 51.

It works well in QGIS to look at objects in local grid but when I save any object in the local grid system the shape files do not save any .prj file with it.

My questions are:

1. Why isn't QGIS saving the .prj file?
2. Is there any way to make QGIS save the .prj file?
3. Is there anyway to convert the WKT format into a .prj file?

WKT custom projection format below:

DERIVEDPROJCRS["KIMG",
    BASEPROJCRS["GDA94 / MGA zone 51",
        BASEGEOGCRS["GDA94",
            DATUM["Geocentric Datum of Australia 1994",
                ELLIPSOID["GRS 1980",6378137,298.257222101,
                    LENGTHUNIT["metre",1]]],
            PRIMEM["Greenwich",0,
                ANGLEUNIT["degree",0.0174532925199433]]],
        CONVERSION["Map Grid of Australia zone 51",
            METHOD["Transverse Mercator",
                ID["EPSG",9807]],
            PARAMETER["Latitude of natural origin",0,
                ANGLEUNIT["degree",0.0174532925199433],
                ID["EPSG",8801]],
            PARAMETER["Longitude of natural origin",123,
                ANGLEUNIT["degree",0.0174532925199433],
                ID["EPSG",8802]],
            PARAMETER["Scale factor at natural origin",0.9996,
                SCALEUNIT["unity",1],
                ID["EPSG",8805]],
            PARAMETER["False easting",500000,
                LENGTHUNIT["metre",1],
                ID["EPSG",8806]],
            PARAMETER["False northing",10000000,
                LENGTHUNIT["metre",1],
                ID["EPSG",8807]]]],
    DERIVINGCONVERSION["Affine",
        METHOD["Affine parametric transformation",
            ID["EPSG",9624]],
        PARAMETER["A0",3644436.5789083,
            LENGTHUNIT["metre",1],
            ID["EPSG",8623]],
        PARAMETER["A1",0.864673183966004,
            SCALEUNIT["coefficient",1],
            ID["EPSG",8624]],
        PARAMETER["A2",-0.50301829055297,
            SCALEUNIT["coefficient",1],
            ID["EPSG",8625]],
        PARAMETER["B0",-7394372.03770256,
            LENGTHUNIT["metre",1],
            ID["EPSG",8639]],
        PARAMETER["B1",0.50301829055297,
            SCALEUNIT["coefficient",1],
            ID["EPSG",8640]],
        PARAMETER["B2",0.864673183966004,
            SCALEUNIT["coefficient",1],
            ID["EPSG",8641]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1]]]

Answer 1

Your custom CRS uses a new WKT definition that was introduced in PROJ 5 or 6. The prj file however is a very old format build by ESRI to define frequently used CRS definitions for shapefiles. It might be that there is no equivalent to your compound transverse mercator with affine transformation in the prj syntax.

UPDATE

After some testing I can confirm your problem. Using GDAL on the command line also does not write the CRS information in the output file. Maybe the GDAL-dev mailing list is the right place to adress this issue.

You can put your WKT definition in a file and name it localCRS.wkt, and use that on the command line with -s_srs or -t_srs to get at least reprojections with ogr2ogr and gdalwarp correctly.