I submitted the question directly to Esri. The support person who responded confirmed that the symbology of a map image layer is not editable in ArcMap.
Here is an excerpt from his email:
1. I downloaded the service from the URL you sent me as a .lyr file and added it to ArcMap, and was unable to change the symbology.
2. I added the service to ArcGIS Online and then opened the service in ArcMap, and again was unable to change the symbology.
Symbology is unable to be changed in map image layers because, rather than being collections of editable feature classes, they are instead pre-rendered collections of map cartography. I am including some documentation on map image layers that describes their makeup as well as common display options for the service type.
https://doc.arcgis.com/en/arcgis-online/reference/map-image-elevation-imagery-layers.htm
https://pro.arcgis.com/en/pro-app/help/data/services/use-map-image-layers.htm
