To watch “Hell’s Kitchen,” the new off-Broadway musical by Alicia Keys that opened Sunday night at the Public Theater, is to experience euphoria followed by enormous frustration over and over again. How can we not feel elated being there for the star-is-born moment of actress Maleah Joi Moon, who makes an earth-shaking professional debut as 17-year-old Ali, a fictional stand-in for Keys? It’s when the singing stops that this show with its sights set on Broadway is no longer on fire.