Madness allows a discarded card to be cast for an alternative madness cost rather than simply being lost to the graveyard. This lets discard effects become a means of deploying spells rather than pure card disadvantage.
Anje Falkenrath can repeatedly discard cards with madness to churn through a deck, while Faithless Looting provides a simple way to discard multiple cards intentionally. Asylum Visitor rewards the empty-hand play patterns that madness decks often produce.