First let me say that's a well thought-out post. It's refreshing to see a break-down like that, whether it is a favorable or unfavorable opinion of aspects of these films.
Here's my response as a fan of these films, but I think we have a lot of common ground on the individual points.
1. Yes, besides his first year out from BB to the end of TDK, he is rarely seen. But we know from the dialogue in the beginning of TDK "I don't like it, not tonight" when the criminal (drug dealer?) sees the batsignal, he has ALREADY had enough of an impact on the city become a legend in that short time. Heck, even the organized crime bosses are too scared of him to have a meeting at night. After he takes the blame for "killing" the city's "hero"-- Harvey Dent, his legend status is further cemented. Not as a good legend by any means, but who in Gotham can ever forget about the guy that killed the white knight. His dark legend is tied inextricable to Harvey's positive legend (at least for the next 8 years). Finally, after all of Gotham (and the world, no doubt watching on TV) apparently witnesses him go up in a nuclear explosion to save the city...his permanent legend is solidified. No one will ever forget the day that Batman gave his life for the city.
2. I really really agree with this point. "I'm not going to kill you, but I don't have to save you." Yes dude, YOU DO HAVE TO SAVE HIM, you're the hero, you're supposed to be better than just letting someone die, even if they are a killer. I absolutely agree with you here. As long as Batman has the ability to save someone, even the villian, he should do it.
3. This is not Nolan's fault. He didn't fire Katie, she made herself unavailable. She had a scheduling conflict. Rumor is Tom Cruise prevented her from signing for the sequel.
4. I believe Batman would have saved Two-Face if he could have. But he had been stabbed by the Joker earlier in the night, then shot (in his armor...but still it powerful enough to knock him down) by Two-Face so he wasn't in top form. Add to that that he also has to save the innocent kid who Two-Face has a 50% chance of shooting if the coin lands bad side up. Batman is not gonna play the odds with a kids life, and there is no time or strength to do some fancy move that both disarms Harvey and saves both him and the kid. So he goes with all he can do, the ugly, brute force tackle. He's got only two arms---one's got to hold on the the 90 lb kid, and one's got to grab the ledge. Or he could have taken his chances and tried to grab the 200lb villianous man with one arm, hoping he would "decide" to also keep holding on to the 90lb kid for Batman (making the total weight on Batman's arm almost 300lb) while trying to hold on to the ledge. He couldn't risk the innocent kid to try to save the non-innocent Harvey.
5. Getting shot by the Batpod cannon may not be as eventful as if there was another big fight like in the sewers and this time Batman was victorious--but we did kind of get that. Batman definitely was beating Bane was about to "win" the fight had Miranda/Talia not surprised him with the old knife to the gut trick. Whether he would have just ripped off his mask or otherwise killed him is debatable. I understand not liking the way he went out, but as for the question of "Why do villains in the films have to die but in the comics they can be allowed to live?" I think it answers itself. In movies, for the most part, there is no intention of telling another story with the villain in a sequel (of course, there are exceptions). Killing off the villain gives finality to a film (or film series) and shows that the specific threat has been vanquished. In serialized comics, you want the villian available in future installments to challenge the hero again and again, endlessly.
6. I agree, this film probably would have benefitted by at least a mention of the Joker. I definitely didn't want to see him recast, whether for a large role or just a cameo as a prisoner though.
8. (there is no #7 above
) I kind of agree with you here, but on the other hand, I did get the feeling of ever increasing chaos while Batman was locked up. Cops who were lucky enough not to be trapped undergroud were being hunted like dogs, Scarecrow was running farce trials, and special forces guys were being killed and strung up from the bridges for all the world to see. That's a pretty scary town to be trapped in.
9. Yes I absolutely agree with this point. Blake has definitely shown he has the rage and the heart to be Batman...he is just missing the extensive training necessary. But someone once said "Training is NOTHING. Will is EVERYTHING."
Like you said, I'd like to believe Bruce will arrange for Blake's training, if not train him himself.
I agree completely with at least 3 or 3.5 of your 8 points, but I think the rest or part of the rest have good justifications for why they are that way. In any case, that was a great post and I enjoyed engaging with it.