Realistically, Sinai's goal now is to get nurses to send their patient home one hour after the physician signs the discharge order. Nurses may communicate discharge instructions to the patient and/or family the day before discharge is expected, and proactively assist with coordinating and arranging for medical equipment and supplies to be in the patient's home when they'll need it.
Games to stimulate behavior change among healthcare workers are not a new idea. For example, in Boston a few years ago, Beth Israel Deaconess Medical Center's emergency room teams launched a game of "Tag, You're It," to catch staff lapsing in their rigorous hand-washing routines. Shamed scofflaws saw their names gracing the dashboard banners of all hospital computer monitors.
So I see nothing wrong with Sinai's campaign to creatively nudge nurses to speed throughput for patients whose continued recovery depends on them sleeping in their own beds, as long as the discharge order has been signed. Keeping patients in the hospital longer than necessary can expose them to additional risk of adverse events such as infections, falls, medication errors and other mishaps.
As Dorothy said as she was transported from the land of Oz, "there's no place like home." As long as you are medically well enough to go there.