Various classical optimization problems are just pure functions. The sorts of things used all over the place in industry (supply chain ops for instance)

If you want real production software, Starbucks Rewards is/was powered entirely by pure Haskell code and made big bucks

Software having complex state actually makes Haskell even better than the competition. Because most state has nuanced rules about its state transitions.

Haskell definitely has more of a learning curve when it comes to dealing with state, but that curve will guide you towards a ceiling mainstream languages can't even approximate.