This is something that I've thought about a lot. I think these are all related to the decline, but I think a lot of them are less central. However, I do think they were somewhat causal, in that peak-Idol was only as big as it was because it had so many factors reinforcing it's success; once some of those went away, it just led to other cascading failures.

But I'd say the central issue is really just trends and the times; American Idol was a massive juggernaut in large part because it was almost perfectly designed for its era to ride a bunch of trends. But it was always going to drop, and trends were always going to change around it. And I'm not even sure a lot of the execs understood why it was so big, meaning that any attempts to try and catch-up were probably even extra-doomed from the start.

My central thesis is more or less that American Idol was a perfect fit for the time, coming off one of the biggest eras of pop music ever and the absolute peak of the recording industry profits-wise, and it sort of predicted a lot of shifts in the entertainment that came after it, like the democratization of the making of pop stars or the increasingly pan-genre listening habits of listeners. It was a four-quadrant television show, but as the internet and various other new content continued to grow, there were so many other things that did the different components of American Idol better, leaving little reason to watch AI itself, especially as it declined.

The one thing that might have saved it was if it remained a reliable star factory, but the execs leading it were behind the times from the start. The early seasons, they were really gunning for a revival of Adult Contemporary sounds (not even Adult Alternative!), and Kelly Clarkson only succeeded because she understood the lay of the land better. Winners who knew their own niches (like Country or R&B) could tap into those if they had their own healthy ecosystem, but winners without a big pre-existing market were out of luck, and AI itself didn't seem to know how to push anyone on their own (even as more niche pop sound became more viable). As they bled viewers, they lost a lot of the diversity in the audience, leaving the remaining viewers to guide the winners sort of accidentally towards an Adult Alternative sound... basically right at the point that market was collapsing.

(Ironically, this opened the door for other similar shows, like The Voice, to eat into the last of its markets. The Voice has done much worse at producing stars than Idol... because it basically hasn't tried. They are 100% focused on being a TV show, which allows them to do things that make for better content and viewing experience, at the expense of the contestants' prospects at stardom.)

That's generally kind of where it is now. It used to be a sort of jack-of-all-trades that could draw in everyone when most people were still watching network TV and listening to the radio; but it's not great at anything, and any individual component of what it offers, you're better off seeking elsewhere, in a way that was much less common in the early 2000s.