He does this. A large part of what Bruce Wayne does during the day is helping Gotham legit.
This is not a Batman problem. All well-known supervillains break out of jail/come back eventually.
Batman stops plenty of villains that never escape. The ones that inevitably do are the ones that are popular and thus MANDATED by the audience to come back. This and the no-kill thing are not Batman specific issues.
To be honest, most longterm problems of the Batman mythos boil down 'because the writers don't let it work'. Gotham isn't allowed to be anything better than the absolute worst hellhole on Earth (ironic, as the silver age it was actually one of the safest cities in the DCU). Villains never make any progress towards becoming better people, certainly not from the facilities intended to actually help them - Harley and Ivy may hover between anti-villains and anti-heroes, but that's not because of the Arkham staff. Bruce's various donations and galas will never provide substantial benefits to the city. And because of comicbook time compression, it won't ever be treated, either in universe or by fans, as though it's been it's been
years since a given villain's last crime, but months at best, leaving the question of 'Why even bother arresting them?' up in the air, particularly as the decades have simply made the villains more and more lethal.
Still, book has potential I'd say. Only hope it doesn't fall into the trap of the Joker not
really reforming after all. Both because it's been done - hi Frank Miller - and because it would likely undermine the premise they're going for. We'll see.