“American Idol” — once the king of all reality shows and the godfather of shows like “The Voice” and “The X Factor” — will be sent off to pasture in 2016. It was 15 seasons old. “Idol” began in 2002 and at its height averaged 30 million viewers a season. Among the singers who owe their careers to the show: Carrie Underwood, Kelly Clarkson, Jennifer Hudson, Jordin Sparks, Ruben Studdard, Fantasia Barrino and Taylor Hicks. Fact is …