If Gotham were really so bad that the police and government were irredeemably corrupt, then maybe Bruce Wayne should have packed his bags and moved somewhere else,
Not gonna happen. Bruce's entire mission in life is to just try to keep what happened to his parents from happening to anyone else in Gotham. That's never gonna change; he is unconditionally dedicated to his city.
because if that were the case, one guy fighting criminals on the streets won't make a difference.(We see that with the criminals who always escape from Arkham-what's the point of Batman putting them away then?)
Except that's bullshit, because Bruce has
made a difference. Batman and his allies have saved hundreds, if not thousands, of lives in Gotham. They literally brought Gotham City back from the dead during the No Man's Land crisis.
Yeah, sure, his mission to prevent any murders from ever happening again in Gotham is quixotic -- but so is the mission of any police department, to try to fight crime. You don't give up on something like that because it's impossible to completely solve; you keep doing it and make it your life's work.