I think some of Idol's initial success comes from when it first aired and the chemistry of the hosts. Post 9/11 and pre-social media, the US hadn't seen anything like it. It hit at just the tight time.
While it has produced a lot of talent that went on to be quite successful, only two winners became huge stars: Kelly Clarkson (S1) and Carrie Underwood (S4). The show ran for 16 seasons.
The TV landscape is littered with musical competition shows that tried to be the next Idol. The Voice is the only one to make it but it has never come close to Idol at its peak. Voice does two cycles per year which I think dilutes its brand. Idol was smart to only do one cycle per year so it became an "event" each time.
I really think they should wait about five years before they trey to relaunch it. Give people a chance to miss it and build anticipation for it. But I also think the entertainment landscape has changed so much in the last few years where though it still may be successful, it will never come near its peak again.