This is a very good question, and one that different writers and filmmakers have approached in different ways. It's not dissimilar to the point that the Punisher is has been pretty much portrayed for the last few decades as definitely needing and wanting a never-ending war against crime, because he is defined by it and without it would potentially feel lost or potentially exact final revenge against himself (suicide) or innocent people (the most interesting and shocking insight of the last decade, in which we learn the Punisher has a recurring nightmare in which the streets are full of the dead criminals he's slain and the war is over, so he turns his gun toward the crowd of civilians and families and says, "If I can't have my family, you can't have yours either...").
Ultimately, however, I think the question misses a crucial point about Bruce's war on crime -- Bruce never believed for a moment that he could truly end crime or "win" the war he wages. He entered it knowing it was an endless war. But he understands the nature of crime and of his war in a particularly nuanced way that few seem to understand: winning this war merely requires FIGHTING the war, nothing more and nothing less. Bruce isn't a fool, and so he understand perfectly well that Batman cannot stop crime, and that nobody else nor everybody else can literally defeat crime. It is the act of engaging the battle and refusing to stop, becoming a symbol of resistance to inspire others to wage war on behalf of society, that is itself the way to "win" the war.
But it's a paradox, because while we need not defeat crime in some literal sense to win, and while the act of defiance and battle itself is "winning," it also requires committing to the battle forever, never giving up, and thus it is an endless commitment to endless war that defines "winning" that war.
So we must recognize that Bruce doesn't "want" his war on crime to end because he always knew it could not "end" in terms of any sort of victory. But more importantly, he doesn't want it to end because he believes that victory is achieved only by refusing to give up in what is otherwise a war that inherently can never be won.
Now, on some deeper level, it is also potentially true that Bruce defines his purpose in life through his waging of war on crime. His scarred psyche, and the fact he so demonstrably defines himself through that traumatic experience, pretty overtly suggest that being Batman is as much a part of who he is as a person -- shaping, then, his entire self-image and personality, the whole way he views his place in the world and indeed how he views the world itself through those eyes -- that it's likely he needs to keep fighting endless against crime, whether he fully realizes it or not (and being Batman, he surely on some level recognizes this need).
But Batman is ultimately entirely unselfish, willing to sacrifice anything and everything if and when necessary for the sake of others. I firmly believe that if he thought it was actually literally possible to end his war with victory that stops crime, saves lives, but leaves him without his war to fight, he'd not even hesitate for a split second to end the war.
More questions on Batman:
- What are all of the items Batman has carried in his utility belt?
- I want to start reading Batman comic books, where should I start?
- Why does Batman save the Joker from falling off to his death in the Dark Knight but let Two Face fall? Doesn't he kill Two Face by doing this?