Agree with most of this, but in a way Batman Begins is also about learning to embrace your fear, have control over it. 'Embrace your worst fear'
At no stage is he told that he needs to lose his fear completely. But he loses the subtlety of that message and by TDKR he's lost his fear of death totally. And he lands himself in the pit, until he re-learns the lesson of his past - why do we fall? - embracing his fear, using it to fuel him.
Well, I thought when he is exposed to the Bats in the cave he over comes his fear of them. It's not just embracing because at first (if I remember correctly) it looks like he's going to have a panic attack from the mere site of bats. This happened before at the monastery when they're hitting his face.
But then he over comes it. The fear is gone. It would have to be considering he becomes what he fear
ed, that was the point. He does get those feelings of anxiety again but that turns out that it's just the effects of the fear toxin (that he recognizes from the monastery), not actually his fear.
And he's certainly told not to be afraid and that everything is alright. Thomas Wayne, Gordon, Alfred, all father figures.
In TDKR, you're right, in order to climb the pit he has to have fear. This fear is not being able to save Gotham though, not his own life. I mean technically, he does fear for his life but that's only because it's the cliched "I'm/he's the only one that can save the city". In his mind, he's the key to Gotham's survival. If he dies failing to make the climb, then the city is done.
But yeah, either way, Gotham is definitely the most important entity in the series. That's what motivates the character, not his parents.
For a future film I want to see Gotham AS the enemy and his parents be the focal point. Thomas and Martha should be the main motivator, not the city. Bruce Wayne shouldn't love or adore Gotham, he should despise it, it took his parents. There's something wrong with it as far as he's concerned.
If there wasn't, Batman wouldn't exist. In most mediums, Gotham isn't a sparkling utopia, if anything it's a decaying dystopia. That's why I didn't really like how the Nolan films portrayed it, as this great city that's worth saving. Metropolis is that clean city and it goes with Superman as a character. Batman is dark and conflicted and Gotham should match that. It SHOULD be "beyond saving", that's the point of Batman. He's there to stop the criminal element, the element that gave birth to him, not clean up the city. If anything, saving someone from losing their parents is more important than Gotham as a whole.