This had me going for several hours, and I just happened across the answer on a video:
Unreal official channel youtube video
At the moment, control rigs and anim blueprints don’t work with inherited skeletal mesh on character blueprints. So just add another skeletal mesh and leave the inherited one blank. Then use control rig on the new skeletal mesh.
I was really lucky to come across this, it really should be a warning in the documentation. Someone could spend days scratching around for no reason.