I would say that Bruce Wayne had to find a reason to live again. The entire movie, from that standpoint, was building up to Bruce Wayne's decision to accept life over death. This was a story about the character becoming human again. The rope was about letting go of whatever is holding you back so that you can move on to the next step in your life. Bruce Wayne needed to do something like that before he could stop being Batman.
Batman was always going to live on. With or without Robin taking over, the symbol would live on forever. But the only way for Batman to be effective was for the legend to be handed over to someone else. I like the idea of "Batman" and "Catwoman" retiring together. Selina Kyle saved him. Quite a while ago I posted that Catwoman is a great villain if handled correctly. She needed to be that crazy chick that makes you go, "**** being a superhero. I'm with her." I don't know if it would have worked if she had been as crazy as I envisioned but it worked with her as his outlet to a more normal life.