Again, again and again huh? Feels like a time loop.
Batman has donated millions to help with poverty actually. For example he funded Leslie Thompkins facility to help the youth of Gotham slums, has a fund that pays for the tuition and even full college fees of many less fortunate people in Gotham, has donated millions to hospitals on several occasions and even tore down a block of slums in Gotham and rebuilt it to be modern for free for its residents.
For mental health, thats why Arkham Asylum exists... although I admit Jeremiah might need to be fired. Also, many of Gotham criminals aren't flat out executed for their numerous murders because they are insane and its illegal to execute a mental patient. Real life serial killers were executed in the past and today many are kept in life imprisonment. Ofc, even thought they are insane, you can't catch a murderer by just asking.
And as for Ivy, while she might care about the environment, it doesn't justify her murdering people.
The police force of Gotham isn't corrupt anymore. It was corrupt, which is part of how Gotham got to be in its current state, but Jim Gordon was able to reform the police force and flush out most bad cops.
