Plakstift,
Unless the customer actually cares that their day crew is covering night standby they won't pony up the jink required for the second crew,ie. low budget companies.
The CARs allows for the use of one crew on 24/7 as long as the flights are emergency flights and that the crew abondons ship for 24 hours as soon as the patient is droppped off where ever that may be. Check your OMA the details are in there.
If you don't like this set up but still don't want to abandon some poor slob that got injured on the rig by declaring crew rest, a little customer education can help. Usually customers that don't get the second crew don't know the rules, regulations or the ramifications of the single crew operation.