How do Gotham's villains collectively challenge Batman, beyond individual physical confrontations?

Gotham's villains pose a multi-faceted challenge to Batman that goes far beyond mere physical combat. Collectively, they represent the systemic corruption, psychological despair, and moral decay that Batman constantly battles. They challenge his detective skills with their elaborate schemes (Riddler), his moral code with their extreme nihilism (Joker), his resourcefulness with their technological prowess (Mr. Freeze), and his physical limits with their brute strength (Bane). Moreover, they continuously push Gotham to the brink, testing its institutions and its people's resilience, forcing Batman to act as both a protector and a symbol of hope in a city perpetually teetering on chaos.