I've been on a sabbatical for about a decade now.
I grew up in LA and have loved the Lakers since the Jerry West days. But since Kobe ran Shaq out of town I've barely rooted for them, or worse. No argument he was a great player and then some in his prime. But he was never a team leader in the true sense of what that means. And I also just have trouble rooting for a rapist.
Having dealt with my disclaimers, here's what's going on in Laker land:
Kobe has always been, and still is, extremely self-centered. The team had to be his team, and he simply can't and won't let that go. For Kobe it's never really been about the Lakers and everything the franchise represents. It's about Kobe. And to him, it's still about Kobe.
As several posters have already stated, this was and is steadily and heavily fed by the Buss family. Jerry was actually pretty solid and balanced until he fell for Kobe. Getting up in years was almost certainly a factor in this. Since he left for the big sky box in the sky, both ownership and management have fallen all over themselves to kiss Kobe's rings. Simply put, the most powerful figure in the Laker organization has been Kobe for quite some time, and still is. He's not going to push himself out. And no one else could even contemplate the idea.
As other posters have mentioned, there are some excellent examples in NBA history of how he should be, and should have already been, adapting his role. Two of the best are -- wait for it -- Kareem and Shaq. What are the chances Kobe would follow their excellent examples? Refer back two paragraphs for the obvious answer.
Kobe will be there, in whatever role he wants, for as long as he wants. Yes, the Lakers are almost certainly multiple years away from making the playoffs again. And the fact that by sticking around, Kobe is increasing that number of years is simply of no concern to Kobe.