Hi! I don't think you miss anything. When you said you activate "Default" Design View Rep, I assumed you were talking about the top-level assembly. Based on the behaviors you are describing, I think the visibility change you made was one of the two cases below.
1) You turn off workplane/sketch visibility within the subcomponent files (not edit-in-place; open in its own window). But, the Design View Reps are not linked to the top-level assembly.
2) You turn off workplane/sketch visibility by editing subcomponents in place or from top-level assembly. The change is only stored within the top-level assembly. The workplane/sketch visibility is still on within the subcomponent files.
Right-click on the part or subassembly which you see visible workplane/sketch -> Representation -> Design View. Is it set to Master or a non-Master DVR? If it is Master, it means you did one of the two workflows above.
The correct way to make sure visibility is consistent across multiple assemblies is to link Design View Rep. Go to Representation -> Design View -> change it to a primary non-Master Design View (Default). Open the subcomponent in its own window. and turn off visibility there -> Save. Now, all assembly with a link to this subassembly Design View Rep will inherit the same behavior (invisible).
Another place to change is the File Open Options (Tools -> App Options -> File). Make sure Default is selected in Design View Rep for Assembly and Part.
Many thanks!