When it comes to Doctors outliving their welcome, I think the other thing you have to consider is the showrunner's influence. Baker's run went on too long, because he was personally tired of the role, but he could still do it justice. The problem was with John Nathan-Turner's (JNT) running of the show. JNT was a very important and very detrimental influence on Doctor Who. When the show succeeded during his run, it was largely in spite of his influence, rather than because of it. With Russel T. Davies (RTD), you had a new direction that worked...for a while, but in all honesty, if you go back and watch the Tennant specials, while the final "I don't want to go" scene is heartrending, the rest of the specials feel...off. Some are too contained to feel truly "special." Some are too bleak in tone. And some are way too bloated.
As a result, I think Tennant picked the right time to leave, and he -- like Davison -- left on a high note without people saying "Man, I'm so glad he's gone." Better to leave folks thinking they could've done with a bit more of you, than with folks thinking "Oh man, he had such a great run....until the end, when it just got boring."
Right now, I don't think the issue is with how long this or that Doctor sticks around. I'm really enjoying Capaldi. I hope he sticks around for a while. But I hope he gets good material to work with, because if he doesn't, then it doesn't really matter how good he is. Moffat, at the moment, is the weak link, I think. His season arcs just don't feel right. And while this season was probably one of his best, it still had issues with so many of the plots being just too...bonkers for my tastes. The moon is a ****ing space egg? And it gets replaced by another space egg? Trees have spontaneously grown at various times and we "forget" it?
There was an interview with Benedict Cumberbatch a little while ago where he apparently spoke with Moffat about understanding Sherlock's background and what makes him tick, what his childhood was like, why he behaves the way he does. Moffat's response was "Couldn't he just be, like, really good at solving stuff? Why does he need a background? Can't he just be really good?" Likewise, Cumberbatch said "We need to give him a weakness like his inability to connect with people." Moffat's response was basically the same "Why? Can't he just be really good? Why's he need a weakness?"
I think those impulses show in Moffat's style with Doctor Who. "Why do we need to ground....anything? Can't we just be off-the-wall loony?" Well, yes, you can, but you have to ground your lunacy in something real. This season, that "something" was the Doctor's relationship with Clara, and the pull she felt between the Doctor and a normal life. And the way the final episode of the season ended? Perfect. I worry that they'll try to add some saccharine or depressing coda to it, and it's just like...dude....know when to fold 'em. This story is done with. Some relationships end like unfinished songs -- with notes that just never get played. You don't need ****ing Santa Claus to show up and make it all better. So, I'm hoping the Christmas special will leave the Doctor and Clara's parting on a dignified level and basically exactly where it was when we saw them part.