That was kind of the point though, in terms of this Batman who had "lost his way". He was not only callous and reckless, but also unsympathetic. All of his focus was on his misguided mission to destroy Superman, rather than on attempting to preserve life or giving these criminals the chance to be rehabilitated/redeemed.
I disagree. The UC has much more of an even balance between Batman and Superman's equally-important arcs, with neither of them truly dominating the story. It's actually much more of a 3-person triangle (Batman, Superman, Lex) than the TC was.
IMO, one of the smartest things this film did was using the MOS Metropolis as the inciting incident that turned Batman against Superman. It gives him a real, legitimate reason to fear Superman and the power he possesses. But that was really just the "straw that broke the camel's back" in terms of pushing Batman over the edge, and part of his distrust from Superman did stem from all of his past experiences and failures as Batman, which is what you just suggested. The movie explicitly states this:
Alfred: You're gonna go to war?
Bruce Wayne: That son of a ***** brought the war to us two years ago. Jesus, Alfred, count the dead... thousands of people. What's next? Millions? He has the power to wipe out the entire human race, and if we believe there's even a one percent chance that he is our enemy we have to take it as an absolute certainty... and we have to destroy him.
Alfred: But he is not our enemy!
Bruce Wayne: Not today. Twenty years in Gotham, Alfred; we've seen what promises are worth. How many good guys are left? How many stayed that way?
The film also paints the picture of a Batman who feels he hasn't accomplished much in his 20-year crusade. He's lost faith in himself and in humanity. He's watched good people turn bad (as expressed above). He's lost a friend and partner (Robin) at the hands of his greatest enemy. He feels that criminals are like weeds, and also describes himself and Alfred as having always been criminals (as opposed to heroes). The existence of Superman and the Metropolis battle (in which he was powerless to stop the senseless violence just as he was powerless to stop his parents' murder) are like big exclamation points on top of his already cynical point of view.
He tells Alfred that killing Superman might be the only thing he does that will matter and it will be his "legacy". He misguidedly feels that this is the only thing he can do to truly make a difference and save people at this point, but subconsciously, I imagine he felt that doing this would fill the void in his soul.
Personally, I think it was a really interesting take on a veteran Batman. It was the portrait of a man who had become a shell of his former self. A man consumed by cynicism who had fallen into darkness and despair, and needed to find a way to crawl back out of that darkness, to be saved from himself, to learn to feel hope again and believe in the inherent goodness of people, to remember the kind of hero he once was and why he ever became Batman in the first place -- not to hunt people, but to save people.
Superman, on the other hand, was someone who had an idealistic point of view, truly believed in the good of others, and had faith in humanity. He was a man trying to do the right thing and help people however he could (both as Clark and as Superman), but he existed in a world that was much more cynical and jaded than himself. In BvS, his idealism is tested every step of the way. He bears witness to people (Lex) committing truly evil acts that he never imagined or expected ("I'm afraid I didn't see it because I wasn't looking"), he deals with the unintended consequences of his good deeds, he's questioned/rejected by his people and told that he shouldn't intervene as he sees fit, he's manipulated, he's hunted and nearly killed by men, the lives of his loved ones are threatened because of him, etc.
And although he does question his idealism and nearly falls into that Batman-level of cynicism at one point ("Nobody stays good in this world"), he doesn't give in or give up. He never loses his faith in humanity, he winds up reaffirming his belief that this world is worth fighting for, and in turn, Superman and his actions are ultimately what save Batman.
