In ArcGIS Online, with other layers in a basemap group, the bottom-most basemap cannot be removed because the Remove option is disabled. Certain layers cannot be moved to the bottom of the basemap layer list.
The bottom-most layer sets the standard for the rest of the layers above it. The bottom-most basemap cannot be removed if the layers above it are Map or Image services that are not cached. Map and Image services can act as additional visuals for the basemap, but cannot be the sole layer representing the basemap.
For instance, if an image layer such as the Terrain: Multi-Directional Hillshade layer is the bottom-most layer, no coordinate system is set for the map, therefore making it not possible to add any layers to the map viewer.
Ensure the bottom-most basemap layer is a tiled or cached image service. The tiled and/or cached services contain information pertaining to the coordinate system.
For more information about hosted tile layers and image service cache, refer to Manage hosted tile layers and Creating an image service cache.