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.
In business domains with strict audit requirements, it’s a peace of mind thing, to know that “side effects” (aka persistence and the mutation of persisted data) are constrained to a tiny and highly testable corner of your code base.
For OSS, the examples that spring to mind for me are RabbitMQ (Erlang) and Pandoc (Haskell).
This is not a "discussion" question, but a "fill my blind spot" question.
I always read how good FP is, and how much better it handles all the complexity. Yet I never see it win from software written with state.
Is there any big and/or complex sofware written in FP that I am overlooking?