With "Enhanced Surveillance", doesn't the controller see the altitude set in the window?
Usually, yes. However there are some types which do not or cannot downlink MCP-selected level. From the report:
There was no downlink from D-ITAN of the flight level selected on the autopilot and so the level-bust could not be anticipated by the controller. D-ITAN did not report on the Thames radar frequency until so close to the point of minimum separation that the controller did not have time to take effective action to resolve the situation.