The inefficiency comes from the power required (= fuel consumed) to run the compressor and accessories and overcome the frictional losses.
If you place an engine in ground idle it will be working at just above self-sustaining with no useful power being produced. The fuel required to keep it running is therefore all wasted.
If fuel is a major consideration on a twin (for example if it is to make the difference between a ditching or making land), purely from a performance point of view it is better to shut down one engine completely and run the other at a high power setting.
As usual, design is a compromise. The designer is torn between over-powering the twin engined aircraft for maximum lift / single engine performance considerations resulting in high fuel consumption or possibly under-powering the aircraft in the event of single engine failure in the quest for better fuel consumption.
Please note that shutting down engines ecxept in a true emergency is not recommended!