Comment by codebje

Well, a reason to care about effects systems is to have a way to specify what a program is doing in a way that lets you calculate and manipulate properties of it (from proofs to optimisations), which generally means static typing and purity.

The curry-howard equivalence is only as useful as the strength of the type system. We ideally want proof irrelevance, that is, any program satisfying the types is sufficient, but while some things remain outside the type system this is only true up to a point (think: time and space costs). Putting effects into types helps this along.